Simulational Methods in Physics

# Seminar Quantum Many-body Dynamics and Nonequilibrium Physics

The seminar takes place on

Wednesdays, 15.15 hrs

At some dates, the seminar will be shifted to a different day.

Venue: Seminar Room of the ITP, Philosophenweg 16.

It covers topics in Cosmology, Elementary particle physics, Quantum Field Theory, and Ultracold atomic gases.

## Upcoming event: Mini-Symposium 'Brain Dynamics', Wednesday 18 June, 14:15 hrs & 15:00 hrs

• 18 June 2013 - Mihai Petrovici (Heidelberg) 14:15 hrs, SR Phil 16
Title: Stochastic Properties of synthetic Brain Circuits

• 18 June 2013 - Markus Karl (Heidelberg) 15:00 hrs, SR Phil 16
Title: Dynamics far from equilibrium at the example of a fermi gas

## This term's talks

• 28 May 2014 - Kenji Morita, (FIAS Frankfurt, Germany) 15:15 hrs, SR Phil 16
Title: Probing the QCD phase boundary with fluctuations of conserved charges
I will discuss properties of fluctuations of conserved charges near the chiral phase transition in QCD. First I will clarify the relation between the phase transition and the conserved charge fluctuations in the context of relativistic heavy ion collision experiments. Second, I will illustrate the property of the net baryon number fluctuations in terms of the underlying probability distribution using a quark-meson model with the functional renormalization group method. Finally I will address the implication for the current experimental data.

• 4 June 2014 - Björn Schenke, (BNL Brookhaven, USA) 15:15 hrs, SR Phil 16
Title: Fluctuating gluon fields, flow, and particle correlations in nuclear collisions

## WS 2013/2014

* 20 Dec 2013 - Emil Mottola, (Los Alamos National Laboratory, USA) 14:00 hrs, SR Phil 16
Title: What's the (Quantum) Matter with Black Holes: Macroscopic Effects of the Conformal Anomaly

• 18 Dec 2013 - Philipp Strack, (Harvard, USA) 15:15 hrs, SR Phil 16
Title: Conserved current correlators in CFT_3's and a new vector boson particle in quantum spin systems

• 11 Dec 2013 - Carlo Pagani, (SISSA Trieste, Italy) 15:15 hrs, SR Phil 16
Title: Functional Renormalization Group and the C-function

• 9 Oct 2013 - Hayder Salman (School of Mathematics, University of East Anglia, Norwich, UK) 15:15 hrs, SR Phil 19 (Note unusual room)
Title: Classical fields methods for Simulating Bose Gases at Finite Temperature
Nonequilibrium phenomena in condensates form an important and growing area of research in low temperature physics. Yet, a systematic theoretical treatment of these class of problems is hindered by the lack of useful approximations that one can introduce to analyse such systems. In this work we consider one particular example of a nonequilibrium system, namely the process of Bose-Einstein condensate (BEC) formation from a strongly nonequilibrium initial condition in a finite-temperature atomic gas. We begin by reviewing recent results obtained within the framework of the classical fields approximation for the idealized scenario of a homogeneous Bose Gas. Using weak turbulence theory, we are able to derive a set of kinetic equations from the classical field equations that provide a nonequilibrium description of the condensation process. Our formulation effectively corresponds to a micro-canonical ensemble. Therefore, it follows that the temperature and the condensate mass fractions are fully determined by the total number of particles and the initial total energy. The results are extended to the more relevant configuration of a trapped BEC. This is achieved by invoking a scale separation argument analogous to that introduced in the local density approximation. However, a novel feature of the work presented is the derivation of new analytical results of the equilibrium properties of the system that goes beyond the Thomas-Fermi approximation that is commonly used in such cases. These analytical results provide a uniformly valid approximation of the condensate density in the vicinity of a nonlinear turning point that is otherwise governed by a second Painleve transcendent.

• 30 Sep 2013 - Hayder Salman (School of Mathematics, University of East Anglia, Norwich, UK) 16:15 hrs, SR Phil 19 (Note unusual room, day and time)
Title: Solitons and Breathers on Quantized Superfluid Vortices
It is well known that quantized superfluid vortices can support excitations in the form of helical Kelvin waves. These Kelvin waves play an important role in the dynamics of these vortices and their interactions are believed to be the key mechanism for transferring energy in the ultra low temperature regime of superfluid turbulence in $^4$He. Kelvin waves can be ascribed to low amplitude excitations on vortex filaments. In this talk I will show that larger amplitude excitations of the vortices can be attributed to solitons propagating along the vortex filament. I will review the different class of soliton solutions that can arise as determined analytically from a simplified vortex model based on the localized induction approximation. I will show, through numerical simulations, that these solutions persist even in more realistic models based on a vortex filament model and the Gross-Pitaevskii equation. As a generalisation of these soliton solutions, I also consider the breather solutions on a vortex filament and illustrate how, under certain conditions, large amplitude excitations that are localized in space {\em and} time can emerge from lower amplitude Kelvin wave like excitations. The results presented are quite generic and are believed to be relevant to a wide class of systems ranging from classical to superfluid vortices. I will also interpret our results on these nonlinear vortex excitations in the context of the cross-over regime of scales in superfluid turbulence.

## SS 2013

• 26 June 2013 - Tomislav Prokopec (TU Darmstadt) 15:15 hrs, SR Phil 16
Title: The final state on de Sitter
I will begin by reviewing de Sitter space, the problems with perturbative quantizations on de Sitter and Starobinsky's stochastic inflation. Next, I will present a non-perturbative technique based on a Legendre transform and show how to construct an effective action based on which one can determine the quantum state of fields at the asymptotic future infinity, which allows for understanding deep infrared (IR) correlators. As an important corollary I will present a proof that an O(N) symmetric scalar theory, that is broken in the UV, undergoes a symmetry restoration in the deep IR. Namely, the strong quantum fluctuations on de Sitter generate a large amount of vacuum energy, thus restoring the symmetry.

• 17 April 2013 - Markus Huber (TU Darmstadt) 15:15 hrs, SR Phil 16
Title: Green functions of Landau gauge Yang-Mills theory from Dyson-Schwinger equations
The gluon and ghost propagators of Yang-Mills theory are useful quantities whose applications range from bound state calculations to investigations of the hase diagram of quantum chromodynamics. I will present results of non-perturbative continuum calculations that take into account also the ghost-gluon vertex self-consistently. The only quantity of the considered system not calculated is the three-gluon vertex for which a new model motivated by lattice results is employed. With this model one can effectively include quantitative two-loop effects so that the propagators are in good agreement with lattice calculations also in the mid-momentum regime, where truncation artifacts were most evident up to now. Furthermore, some preliminary results at non-zero temperature will be presented.

## WS 2012/13

• 26 March 2013 - Sergej Moroz (University of Washington) 15:15 hrs, SR Phil 16
Super Efimov effect
Three-body problems are notoriously difficult to solve both in classical and quantum physics. More then four decades ago Vitaly Efimov found a surprisingly simple solution of a quantum mechanical problem of three resonantly interacting non-relativistic bosons. He discovered an infinite tower of geometrically spaced three-body bound states arising at the two-body resonance. Only recently the advent of beautiful experiments with ultracold atoms allowed us to see the signatures of the Efimov effect experimentally. It turns out that in two spatial dimensions resonantly interacting non-relativistic fermions form few-body bound states similar to the ones predicted by Efimov. I will explain how this super Efimov effect can be derived from the renormalization group calculation and describe its possible implications to the many-body physics of topological chiral superfluids.

• 31 October 2012 - Leticia Palhares (U Heidelberg) 15:15 hrs, SR Phil 16
QCD under strong magnetic fields

• 4 October 2012 - Christian Korff (U Glasgow, UK) 14:15 hrs, SR Phil 19
Computing fusion coefficients via the discrete Bose gas
We consider a particular discretisation of the Bose gas with contact interaction (the quantum nonlinear Schroedinger model) and relate it to an exactly solvable statistical mechanics model of random walkers on a cylindrical square lattice. The transfer matrix of the latter model generates a set of commuting Hamiltonians for the discrete Bose gas and their spectrum and eigenvectors can be computed explicitly using the Bethe ansatz. The eigenvectors can be naturally interpreted as the idempotents of an algebra which defines a 2D quantum topological field theory. In the strong coupling limit this allows one to compute the fusion coefficients of Wess-Zumino-Witten field theory in terms of a simple hopping algorithm of bosons on a circular lattice.

• 26 September 2012 - Fujii, Hirotsugu (U Tokyo, Japan) 15:15 hrs, SR Phil 16
Color Glass Condensate approach to pA collisions at the LHC
We will report the current predictions to the particle productions in pA collisions at LHC in the framework of the Color Glass Condensate. For the nucleus part, we use the numerical solutions of the BK evolution with running coupling regularized smoothly in the IR region. We update the description from RHIC and the predictions to the LHC.

## SS 2012

• 1 August 2012 - Reinhard Alkofer (U Graz, Austria) 15:15 hrs, SR Phil 16
Electron-Positron Pair Creation in Structured Pulses of Electric Fields
Electron-positron pair production for short laser pulses with multiple time-scale sub-structures is considered in the nonperturbative regime (Schwinger pair production). After a short discussion of the underlying mechanism the non-equilibrium quantum kinetic approach is introduced. Results for the momentum spectra of the created electron-positron pairs are presented. These may lead to new probes of light pulses at extremely short time scales. Considering suitably combined time-scales and field strengths can lead to a significant enhancement in the production rates (dynamically assisted Schwinger effect) and interferences in the obtained spectra. Recent attempts to apply optimal control theory for pulse shaping are reported. Last but not least, some results on pair creation in space- and time-dependent fields are presented.

• 11 July 2012 - Neda Sadooghi (Teheran, Iran) 15:15 hrs, SR Phil 16
The effect of external magnetic fields on the dynamics of neutral mesons at finite temperature
The effect of external magnetic fields on the phase diagrams of a two-flavor NJL model at finite temperature and chemical potential will be discussed in detail. Using an appropriate derivative expansion up to second order, the effective action of a two-flavor NJL model will be determined, and the energy dispersion relations of the neutral mesons, including non-trivial form factors, will be computed. Moreover, we will explore the temperature dependence of the pole and screening mass as well as the directional velocity of neutral mesons for various fixed magnetic fields. We will show that neutral mesons travel, in the transvesre direction with respect to the direction of the external magnetic field, at speed larger than the speed of light.
Ref.: arXiv:1206.6051.

• 6 July 2012 - Rob Pisarski (Brookhaven, NY) 14:00 hrs, SR Phil 16 (Note unusual day and time)
Matrix Model of deconfinement

• 20 June 2012 - Makoto Tsubota (Osaka, Japan) 15:00 hrs (sharp), SR Phil 16 (Special CQD seminar)
Quantized Vortices and Quantum Turbulence
We discuss recent important topics in quantum fluid dynamics and quantum turbulence [1]. Quantum turbulence (QT) was discovered in superfluid 4He in the 1950s, but the field moved in a new direction starting around the mid 1990s. Quantum turbulence is comprised of quantized vortices that are definite topological defects arising from the order parameter appearing in Bose-Einstein condensation. Hence QT is expected to yield a simpler model of turbulence than does conventional classical turbulence (CT). The innovation has come from two facts. First, the scientists have started to consider the comparison between QT and CT chiefly in superfluid helium. For example, the Kolmogorov spectrum, which is the most important statistical law in turbulence, is confirmed experimentally and numerically in superfluid helium. Secondly, the realization of atomic Bose-Einstein condensation in 1995 has proposed another important stage for this issue. A general introduction to this issue and a brief review of the basic concepts are followed by the recent developments of the studies of QT. I will discuss some of the interesting topics. (1) Vortex lattice formation in a rotating Bose-Einstein condensate [2]. (2) Energy spectra of QT [3]. (3) Hydrodynamic instability and QT in atomic Bose-Einstein condensates [4].

[1] Progress of Low Temperature Physics Vol.16, eds. W. P. Halperin and M. Tsubota (Elsevier, 2008).
[2] M. Tsubota, K. Kasamatsu and M. Ueda, Phys. Rev. A 65, 023603 (2002).
[3] M. Kobayashi and M. Tsubota, J. Phys. Soc. Jpn. 74, 3248 (2005).
[4] M. Tsubota and K. Kasamatsu, arXiv:1202.1863.

• 6 June 2012 - Mario Mitter (Graz, Austria) 15:15 hrs, SR Phil 16
The Chiral Transition in a (2+1)-Flavor Quark-Meson Model with Fluctuations
The chiral phase transition is investigated in a $(2+1)$-flavor quark-meson model truncation within the non-perturbative functional renormalization group. The influence of a temperature independent $U_A(1)$ violating 't Hooft determinant is investigated in the light chiral limit. Critical exponents agreeing with the $O(4)$ universality class are obtained in the light chiral limit with determinant.

• 23 May 2012 - Axel Maas (Jena, Germany) 15:15 hrs, SR Phil 16
Non-perturbative aspects in Higgs physics
It is a remarkable fact that an interaction as weak as QED can sustain bound states. A similar feature naturally can also be expected for the weak interactions. In fact, it has been conjectured in the late seventies that to leading order in an expansion in the Higgs condensate such bound states will have the same mass as the corresponding elementary particle at tree level. Using non-perturbative numerical lattice simulations, evidence will be shown that this holds approximately true even beyond this leading order, provided an adequate renormalization scheme is chosen. This also resolves the apparent paradox that while the Higgs mass itself is both scheme and renormalization point dependent, the peak observed in a cross section is not. Interpreting the actual resonance as a Higgs-Higgs bound state dual to the elementary state gives a physical explanation for the presence of this peak. A similar construction can also be made for the W boson. Such an interpretation of the actually observed resonance peaks as bound states implies necessarily the possibility for excited states. If these should be sufficiently stable, they can show up as 'new particles' in the LHC data, even if they are completely within the standard model. Using once more lattice simulations some ideas are provided for the properties of such an excited Higgs.

• 16 May 2012 - Tomislav Prokopec (Utrecht, Netherlands) 15:15 hrs, SR Phil 16
On symmetry breaking in de Sitter space
Not much is understood on symmetry breaking in de Sitter space, which often serves as a model space for inflation. I will consider symmetry breaking in an O(N) symmetric scalar field model in the mean field approximation. The symmetry gets broken to O(N−1), and the transition is of first order. Analogously to the BEH and PQ mechanisms, the would-be Goldstone bosons acquire a mass, such that there is no symmetry left in the vacuum. A better understanding of symmetry breaking in de Sitter can be helpful to have a better control of inflationary dynamics and of post-inflationary preheating.

• 18 April 2012 - Ludwig Faddeev (St. Petersburg) 15:15 hrs @ SR Phil 16 (Special Seminar)
Alternative formulation for the Einstein Theory of Gravitation

• 21 March 2012 - Mariusz Puchalski (Univ. of Poznan, Poland) 15:15 hrs @ SR Phil 16
Calculations for lithium-like systems with correlated functions
The analytical evaluation of four-particle integrals, performed in 1987 by Fromm and Hill [1] opened up the possibility for high-precision variational calculations of four-particle systems in a basis of exponential functions of all interparticle distances. The variationally determined nonrelativistic wave function has correct analytic properties and can be used in the accurate calculations of relativistic and QED effects [2], such as that in transition frequencies, isotope shifts, or hyperfine splittings [3]. The correct analytic properties are essential in obtaining higher order relativistic effects, where the standard approaches fail. We demonstrate our method on several examples for the lithium-like low-lying states. Together with the high-precision approach in Hylleraas basis [4], we are aiming to determine mα^6 and mα^7 effects in the fine and hyperfine structure of lithium-like systems.

[1] D.M. Fromm and R.N. Hill, Phys. Rev. A 36, 1013 (1987).
[2] M. Puchalski, D. Kedziera, K. Pachucki, Phys. Rev. A 80, 032521 (2009), Phys. Rev. A 82, 062509 (2010), Phys. Rev. A 84, 052518 (2011).
[3] R. Sanchez, et al., N. J. Phys. 11, 073016 (2009), W. Nörtershäuser, et al., Phys. Rev. A 83, 012516 (2011).
[4] M. Puchalski, K. Pachucki, Phys. Rev. A 73, 022503 (2006), Phys. Rev. A 78, 052511 (2008), Phys. Rev. A 79, 032510 (2009).

## WS 2011/12

• 15 Febrary 2012 - Laith H. Haddad (Golden, CO) 15:15 hrs @ SR Phil 16
The nonlinear Dirac equation: Relativistic vortices and experimental realization in Bose-Einstein condensates
We study the relativistic generalization of mean-field theory for Bose-Einstein condensates. Condensates in a honeycomb optical lattice are described by the nonlinear Dirac equation (NLDE) in the long wavelength, mean field limit [1]. We introduce relativistic linear stability equations (RLSE) necessary to determine lifetimes for generic solutions of the NLDE [2]. Combined, the NLDE and RLSE form the relativistic generalization of the Gross-Pitavskii and Bogoliubov-de Gennes equations, respectively. We focus here on the large proliferation of relativistic vortices which appear as solutions of the NLDE, most of which we obtain in analytical form. In the case of unit winding number, we obtain the Mermin-Ho and Anderson-Toulouse vortices. For higher winding, we obtain topological as well as non-topological vortices in the form of an asymptotic Bessel solution, as algebraic closed-form solutions, and using standard numerical shooting methods. We solve the RLSE for our localized solutions and find anomalous as well as dynamically unstable modes in the linear spectrum for most solutions. Using data for 87Rb for our vortex backgrounds, we find the imaginary parts of the linear eigenvalues to be two to three orders of magnitude smaller than the interaction strength which give vortex lifetimes ∼ 10 s [3]. To realize the nonlinear Dirac structure in the laboratory, we propose using Bragg scattering and a Laguerre-Gaussian laser beam to induce the two-photon Raman transitions in 87Rb needed to create our vortex solutions.

[1] L. H. Haddad and L. D. Carr, The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries, Physica D: Nonlinear Phenomena, 238, 1413 (2009). http://arxiv.org/pdf/0803.3039v1
[2] L. H. Haddad and L. D. Carr, Relativistic Linear Stability Equations for the Nonlinear Dirac Equation in Bose- Einstein Condensates, Europhysics Letters Jan. 2011, 94, 56002 (2011). http://arxiv.org/abs/1006.3893
[3] L. H. Haddad, K. M. O’Hara, L. D. Carr, The nonlinear Dirac equation: Relativistic vortices and experi- mental realization in Bose-Einstein condensates, (to be submitted to Phys. Rev. Lett., Feb. 2012).

• 08 February 2012 - Michael G. Schmidt (Heidelberg) 15:15 hrs @ SR Phil 16
On entropy and decoherence in QFT: an exercise with Kadanoff-Baym Equations

• 25 January 2012 - Harmen Warringa (Frankfurt) 15:15 hrs @ SR Phil 16
Vortex formation in a rotating two-component Fermi gas

• 23 January 2012 - Roman Hennig (Heidelberg) 11:30 hrs @ SR Phil 16
Shear Viscosity of an ultracold Bose gas

• 11 January 2012 - Philipp Strack (Harvard) 15:15 hrs @ SR Phil 16
Tunable quantum glasses and phase transitions of atoms and photons: first testable predictions for glassy physics with many-body cavity QED
Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. In this talk, we argue that realizations of the Dicke model with variable atom-photon couplings can give rise to a ground state phase diagram exhibiting quantum phase transitions between paramagnetic, ferromagnetic, and a spin glass phase. These quantum optics realizations of quantum glasses are distinctive to condensed matter systems and provide new opportunities for glassy physics with many-body cavity QED. The photon-mediated random couplings between the atomic qubits (Ising spins) are truly long-ranged and the theory for these systems remains analytically tractable. We compute atomic and photon spectral response functions across this phase diagram, and outline how our predictions can be observed in experiments. References: arXiv:1109.2119, accepted to Physical Review Letters

• 14 December 2011 - Maik Stuke (Bielefeld) 15:15 hrs @ SR Phil 16
First second of lepton asymmetries
In my talk I summarize the influence of lepton asymmetries on the evolution of the early Universe, in particular on big bang nucleosynthesis, the cosmic QCD transition, and the freeze out of the most promising Dark Matter candidate, the WIMP. The lepton asymmetry l is poorly constrained by observations and might be orders of magnitudes larger than the observed baryon asymmetry b ~ 10^(-10), |l|/b < 10^9. I show that lepton asymmetries large compared to the tiny baryon asymmetry, might influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the mu_b - T phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. However, for large lepton asymmetry, the order of the cosmic transition remains unknown. I will also show, that a large asymmetry in one or more lepton flavour changes relic abundance of WIMPs. For an asymmetry of l_f = 0.1 in all three flavour we found a decrease of the relic WIMP abundance for a given freeze out temperature of 20 percent.

• 5 December 2011 - Simon Gardiner (Durham, UK) 11:30 hrs @ SR Phil 16
Classical and quantum properties of bright matter-wave solitons in an attractively interacting atomic Bose-Einstein condensate
When a dilute gas of bosonic atoms is cooled to degeneracy it passes through a quantum phase transition to form a Bose-Einstein condensate (BEC). Beyond this point the properties and dynamics of the BEC can frequently be very well described by a nonlinear classical field equation, the so-called Gross-Pitaevskii equation, which is capable of supporting a variety of excitations, including solitons and vortices. Bright solitons (non-dispersive waves that are robust to collisions) are of particular interest because they have attractive stability properties for potential applications in metrology and interferometry. Formally, such solitons exist as solutions to a 1D nonlinear Schrodinger equation with a focusing (attractive) cubic nonlinearity, in the absence of any confining potential. In my talk I will discuss such questions as:
- How 1D is 1D?
- How soliton-like is a trapped soliton?
- How classical-like is the (fundamentally quantum) system?
- How can solitons be used in interferometry?

• 28 November 2011 - Jan Schole (Heidelberg) 11:30 hrs @ SR Phil 16
Turbulence in an ultra-cold Bose gas in two dimensions
The dynamics of an ultra-cold Bose gas is analyzed in two dimensions. Starting with an initial state far from equilibrium the time evolution is simulated using the Gross-Pitaevskii-equation in the context of the Truncated Wigner approximation. The evolution and the decay of turbulence are described. One focus are the spectra of the occupation number n(k) and the kinetic energy in momentum space. The formation of a stationary state with n(k) folling a power law is observed. Using the point vortex model, the scaling for small wave numbers can be explained in terms of a random distribution of vortices and antivortices. The time evolution of the vortex density and of the vortex-antivortex correlations are analyzed. In all simulations the decay of the vortex density shows a crossover between two regimes which are governed by a scaling law Nv ˜ t^-xi. Motivated by the analysis of vortex-antivortex correlations it is proposed, that the crossover can be explained by the fast mutual annihilation of the vortex-antivortex pairs at short distances. In comparision with the time evolution of the vortex density it is demonstrated that the condensate grows with the decay of the vortices.

• 14 November 2011 - Maximilian Schmidt (Heidelberg) 11:30 hrs @ SR Phil 16
Solitonic States in the Far-from-equilibrium Dynamics of an Ultracold Bose Gas
Non-equilibrium time evolution of an ultracold Bose gas in one spatial dimension is studied. The gas is con ned by harmonic potentials and exposed to an interaction quench and evaporative cooling. We simulate the system numerically by solving a classical fi eld equation for stochastically sampled initial states on a discrete lattice. Quasistationary states are found in the evolution of the spectra, which are a signature of turbulent behaviour. We show that they can be explained by analytical calculations within a model for randomly distributed solitons. Furthermore, we investigate the evolution of the number of solitons and find that the decay of solitons is enhanced by the cooling. In addition, we study a collision of two cigar-shaped Bose-Einstein condensates as an example of a quasi 1D system where transverse excitations lead to the formation of solitons. The creation of a varying number of solitons is observed and discussed.

• 19 October 2011 - Toru Kojo (Bielefeld)
Quarkyonic Matter and Chiral Spirals
First I will explain basic concepts and motivations to consider "Quarkyonic matter" at T=0 in which bulk properties are saturated by quark degrees of freedom, nevertheless excitations are confined. Nuclear matter, conventional deconfined quark matter, and Quarkyonic matter are classified by means of 1/Nc expansion. I will shortly illustrate its (1+1) dimensional example, 't Hooft model at finite density. Next I will discuss chiral symmetry in (3+1)-D Quarkyonic matter which is broken by the formation of chiral spirals. Its extension to the "interweaving chiral spirals" and its relation to the baryon number modulation is briefly discussed.

• 17 October 2011 - Jan Zill (Heidelberg) 11:30 hrs @ SR Phil 16
Exact many-body quantum dynamics in the Lieb-Liniger model
The physics of ultra-cold bosons in one spatial dimension is investigated by solving the time-dependent many-body Schrödinger equation. For this purpose, the Lieb-Liniger model is employed. It describes ultracold gases interacting via s-wave scattering. The model is exactly solvable by means of the Bethe ansatz and the system described by it has been experimentally realized in recent years. In the first part, the focus is set on the ground state properties of the homogeneous system. The stationary properties are studied in terms of correlation functions and in the entire repulsive inter-particle interaction range. A method to obtain the energy spectrum is developed. This lays the foundation for studying time-dependent phenomena in the Lieb-Liniger model. The dynamics of a non-equilibrium initial state is investigated. Relaxation of the momentum distribution and the first-order density matrix is observed for as few as two particles.

• 28 September 2011 - Jan Schröder (Dortmund)
Unitarity in Fixed Point Gravity
Unitarity constraints in a Fixed Point Gravity scenario with compact extra dimensions and a TeV sized fundamental Planck mass are examined by calculating single Graviton exchanges in Higgs-Higgs-scattering.

## SS 2011

• 01 June 2011 - Sascha Zöllner (Niels Bohr Institute)
Impurities in a Two-Dimensional Fermi Gas
The state of an impurity atom immersed in a quantum gas is a fundamental model of many-body physics. In this talk, I discuss how such a simple model can tell us something about highly imbalanced Fermi gases - i.e., a Fermi gas of one component with a low concentration of a “minority” species added. The picture that emerges is that: For weak attraction between impurity and majority atoms, the state is well described by an impurity atom dressed by particle-hole excitations of the Fermi gas (often called a “polaron”). For stronger attraction, a sharp transition occurs to a simple “dimer” state of the impurity with one majority atom - at least in three dimensions. I argue that in lower dimensions, the situation is more subtle, and particle-hole fluctuations play a crucial role. This also has implications for small ensembles of impurities, where quantum statistics come into play.

• 30 May 2011 - Katharina Jürges
Modelling interacting bosons in disordered optical lattices – an introduction

• 11 May 2011 - Falk Bruckmann (Regensburg)
Title

## WS 2010/11

• 03 February 2011 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 8. session. Thu 10:00 hrs!

• 02 February 2011 - Ofir Alon (Haifa)
Non-equilibrium quantum dynamics of attractive and repulsive ultra-cold Bose gases

• 31 January 2011 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 7. session. Mon 11:30 hrs!

• 24 January 2011 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 6. session. Mon 11:30 hrs!

• 13 December 2010 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 5. session. Mon 11:30 hrs!

• 08 December 2010 - Tom Judd (Tübingen)
Finite temperature interactions between cold atoms and nanostructures

• 06 December 2010 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 4. session. Mon, 11:30 hrs!

• 01 December 2010 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 3. session. 15:30 hrs!

• 22 November 2010 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 2. session. (Mon 11:30 hrs!)

• 17 November 2010 - Heinz Horner (Heidelberg)
Turbulence
Block lecture. 1. session. (SR Phil 19!)

• 24 November 2010 - Andreas Rodigast (Berlin)
Running Couplings in perturbative Quantum Gravity

• 10 November 2010 - Hans-Jürgen Pirner (Heidelberg)
Describing the LHC Fireball as a black hole in 5 dimensions

• 8 November 2010 - Jens O. Andersen (Trondheim)
Quasiparticles and hard-thermal-loop perturbation for a quark-gluon plasma
We calculate the thermodynamic functions of a quark-gluon plasma for general N_c and N_f to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant.We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T~2T_c.

## SS 2010

• 19 May 2010 - Alexej Weber (Heidelberg)
Casimir Effect in the Worldline Formalism
In my talk I will discuss the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. The worldline approach used allows the precise computation of Casimir energies in arbitrary geometries. I show the dependence of the Casimir force on the separation parameter and temperature T, and present Casimir phenomena which are dominated by long-range fluctuations. I demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. Whereas the high temperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior.

## WS 2009/2010

• 13 January 2010 - Julien Serreau (Paris)
Decoherence and thermalization of a pure quantum state in quantum field theory
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N-expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. Restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, the system is described by an effective (reduced) density matrix which, unlike the full density matrix, has a nontrivial time evolution. In particular, starting from a pure quantum state, we observe the loss of putity/coherence and, on longer time scales, thermalization of the reduced density matrix. We point out that the physics of decoherence is well described by classical statistical field theory.

• 16 December 2009 - Jürgen Schaffner-Bielich (Heidelberg)
An inflationary QCD phase transition in the early universe?
We explore a scenario that allows for a strong first order phase-transition of QCD at non-negligible baryon number in the early universe and its possible cosmological observable consequences. The main assumption is a quasi-stable QCD-vacuum state that leads to a short period of inflation, consequently diluting the net baryon to photon ratio to it's today observed value. A strong mechanism for baryogenesis is needed to start out with a baryon asymmetry of order unity, e.g. as provided by Affleck-Dine baryogenesis. The cosmological implications are direct effects on primordial density fluctuations up to dark matter mass scales of 1 - 10 solar masses, change in the spectral slope up to mass scales of 10**6 - 10**7 solar masses, production of primordial magnetic fields with initial strength up to 1012 Gauss and a gravitational wave spectrum with present day peak strain amplitude of at most h_c = 4.7 * 10-15 around a frequency of 4*10-8 Hz. The little QCD inflation scenario could be probed with the upcoming heavy ion research facility FAIR at GSI, Darmstadt.

## SS 2009

• 8 July 2009 - Neda Sadooghi (Tehran)
The Speed of Sound in a magnetized Quark-Gluon-Plasma

• 1 July 2009 - Svend Domdey (Heidelberg)
Testing the Scale Dependence of the Scale Factor in Double Dijet Production at the LHC
The scale factor is the effective cross section used to characterize the measured rate of inclusive double dijet production in high energy hadron collisions. It is sensitive to the two-parton distributions in the hadronic projectile. In principle, the scale factor depends on the center of mass energy and on the minimal transverse energy of the jets contributing to the double dijet cross section. Here, we point out that proton-proton collisions at the LHC will provide for the first time experimental access to these scale dependences in a logarithmically wide, nominally perturbative kinematic range of minimal transverse energy between 10 GeV and 100 GeV. This constrains the dependence of two-parton distribution functions on parton momentum fractions and parton localization in impact parameter space. Novel information is to be expected about the transverse growth of hadronic distribution functions in the range of semi-hard Bjorken x (0.001 < x < 0.1) and high resolution Q^2. We discuss to what extent one can disentangle different pictures of the $x$-evolution of two-parton distributions in the transverse plane by measuring double-hard scattering events at the LHC.

• 30 June 2009 - Erhard Seiler (Munich)
The complex Langevin method: Successes and Difficulties
The complex Langevin method provides in principle a solution to the problem of simulating quantum field theories with complex action. It has also been shown to work remarkably well in various examples. On the other hand it runs into unexpected difficulties in other cases. I will discuss the mathematical basis of the method, as far as it exists, and point out open mathematical and as practical problems.

• 24 June 2009 - Tereza Mendes (Sao Paulo)
Infrared Propagators and Confinement: a Perspective from Lattice Simulations
Lattice studies of the infrared behavior of gluon and ghost propagators may offer a crucial test of confinement scenarios in Yang-Mills theories. However, finite-volume effects clearly become an important issue as the infrared limit is approached. We study the Landau-gauge SU(2) case using data from the largest lattice sizes (i.e. smallest momenta) to date. By imposing rigorous constraints to gain control over the infinite-volume limit, we gain a better understanding of the propagators in terms of more general quantities.

• 17 June 2009 - Jorge Noronha (Columbia University)
Can AdS/CFT be used to describe soft and hard phenomena observed at RHIC?
We show that five-fold constraints due to (1) the observed nuclear modification of heavy quark jets measured via non-photonic electrons, $R_{AA}^e(p_T \sim 6\,{\rm GeV})$, (2) the elliptic transverse perfect fluid'' flow of low transverse momenta pions, $v_2(p_T\sim 1\;{\rm GeV})$ in noncentral Au+Au collisions at 200 AGeV, (3) the entropy density deficiency, $S/S_{SB}$, of strongly coupled Quark-Gluon Plasmas (sQGP), (4) the observed entropy inferred from the pion multiplicity $dN_\pi/dy$, and (5) causal response are analytically related in a class of gauge/string dual models of sQGP dynamics and remarkably compatible with the data with t'Hooft and Gauss-Bonnet parameters in the range of $\lambda\approx 10-25$ and $0< \lambda_{GB}< 0.09$. In addition, the observed five-fold correlation is shown to favor color glass condensate over Glauber initial sQGP conditions within current systematic errors.

• 13 May 2009 - Christian Fischer (Darmstadt)
Deconfinement phase transition and the quark condensate
We study the dual quark condensate as a signal for the deconfinement phase transition. This order parameter for center symmetry has been defined recently by Bilgici et al. within lattice QCD. In this work we determine the dual condensate with functional methods using a formulation of the Dyson-Schwinger equations for the Landau gauge quark propagator on a torus. We study the chiral and deconfinement phase transitions of quenched QCD by related suszeptibilities. The gauge fixed functional formalism yields similar results for the deconfinement transition as lattice QCD.

• 29 April 2009 - Bertrand Delamotte (Paris U., VI, LPTL)
Momentum dependence of correlation functions:
calculations and results obtained for systems at or out-of-equilibrium

## WS 2008/09

• 28 Jan 2009 - Tobias Paul (Heidelberg)
Nonlinear transport of Bose-Einstein condensates - from superfluidity to Anderson Localization

• 21 Jan 2009 - Lev Ananikyan (Heidelberg)
Entanglement in the Heisenberg model

• 8 Jan 2009 - Szabolcs Borsanyi (Wuppertal) 16:15 hrs @ SR Phil 16
(in the frame of the Teilchentee seminar)
From cosmic strings to oscillons

• 10 Dec 2008 - Thomas Gasenzer (Heidelberg) 13:30 hrs @ SR Phil 16
(in the frame of the Werkstatt-Seminar Hochenergiereaktionen)
Non-equilibrium coherence dynamics in one-dimensional Bose gases

• 3 Dec 2008 - Denes Sexty (Darmstadt)
Recent Results of Stochastic Quantisation

## SS 2008

• 18 Jul 2008 - Daniel Spielmann (Heidelberg)
Aspects of Infrared QCD from Stochastic Quantization on the Lattice
In order to understand the mechanism of confinement in QCD, the infrared behavior of Green's functions in Landau gauge has been thoroughly investigated in recent years. Confinement scenarios, such as Gribov-Zwanziger and Kugo-Ojima, have implications for the ghost and gluon propagator in the IR. However, results from continuum methods such as the functional renormalization group and Dyson-Schwinger equations, while corroborating these predictions, contradict the infrared asymptotics found in lattice simulations. After reviewing this situation, I will outline the approach of stochastic quantization including Zwanziger's concept of stochastic gauge fixing as a possible remedy. This method has already previously been adapted to lattice gauge theory in order to tackle the Gribov problem. I will present first results obtained thus for the Landau gauge ghost and gluon propagator, also in the lower-dimensional case, and compare with standard gauge fixing. In addition, I will show numerical evidence on how the stochastic method samples configurations, e.g. from the spectrum of the Faddeev-Popov operator. This is of interest as the Gribov-Zwanziger picture predicts a certain part of configuration space to be responsible for confinement.

• 25 Jun 2008 - Matthias Ohliger (Berlin)
Diagrammatic Green's Function Approach to the Bose-Hubbard Model
Following an approach first used by W. Metzner in the context of electrons in conductors we use a diagrammatic hopping expansion to calculate both grand potential and finite temperature Green's functions of the Bose-Hubbard Model used to describe Bosons in an optical lattice. This allows us to reconstruct in a qualitative way the time-of-flight absorption pictures, which are taken after the optical lattice is switched off. Furthermore, the technique makes summations of subsets of diagrams possible, leading to non-perturbative results needed to locate the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by Monte-Carlo simulations of the Bose-Hubbard model. In the second part, we examine the superfluid-Mott insulator transition of spin-1 Bosons in an optical lattice where we extend previous mean-field studies to finite temperature. We find an interesting asymmetry between Mott-states with even and odd filling factors which continuously disappears for higher temperature.

• 6 Jun 2008 - Sascha Zöllner (Heidelberg) 14:00 hrs @ SR Phil 16
Fermionizing One-dimensional Bosons: Mechanism and Tunneling Dynamics

• 29 May 2008 - L. Mühlbacher (Freiburg) 14:15 @ SR Phil 19
(In the frame of the Seminar on Theory of Complex Systems)
Real-time Quantum Monte Carlo simulations for non-equilibrium systems: A diagrammatic path-integral approach

## WS 2007/08

• 20 Feb 2008 - Svend Domdey (Heidelberg)
Gluon jet fragmentation in the Quark-Gluon Plasma

• 6 Feb 2008 - Valya Khoze (Durham)
Aspects of Seiberg Duality and its Applications

• 21 Jan 2008 - David Hutchinson (Otago/Paris) 11:00 hrs @ KIP, SR 2.402
(in the framework of the Journal-Club Seminar on Ultracold Gases)
Effects of Disorder in Ultra-cold, dilute gases
The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of both theoretical and experimental interest. These systems offer unprecedented control over inter-particle interactions, imposed potentials and the level of disorder in the system as compared to their condensed matter analogues. The two-dimensional (2D) case is of particular interest. The prevailing view has been that in the 2D electron gas there is no metallic state, but recent experiments are suggestive of a metal-insulator transition in very dilute systems. We investigate theoretically the possibility of observing strongly localized states, corresponding to the insulating phase, review the experimental position in the field in the dilute 2D gas and discuss potential future experiments.

• 11 Jan 2008 - Lorenz von Smekal (Adelaide) 14:30 hrs @ SR Pw 16
Modified Lattice Landau Gauge
The infrared behaviour of QCD Green's functions in Landau gauge has been focus of intense study. Different non-perturbative approaches all lead to the same overall picture. These include Dyson-Schwinger Equations, Functional Renormalisation Group Equations, Stochastic Quantisation, and Lattice Landau Gauge Simulations. Finite volume effects are being increasingly well understood. I will briefly review the situation. But do covariant gauges have the potential to be truly non-perturbative in the first place? BRST constructions have long been blamed for only being perturbatively well defined. Lattice definitions are plagued by the Neuberger problem. I will describe ways to avoid this problem, and the modifications necessary to implement these, including first results from Monte-Carlo simulations using a modified lattice Landau gauge.

• 17 Dec 2007 - Peter Schlagheck/Tobias Paul (Regensburg/Orsay) 11:00 hrs @ KIP, SR 2.402
(in the framework of the Journal-Club Seminar on Ultracold Gases)
P. Schlagheck: Nonlinear transport of Bose-Einstein condensates through disorder
T. Paul: Bose-Einstein condensates in presence of defects and disorder
Superfluidity and Anderson localization are genuine many-body manifestations of quantum coherence which are nowadays revisited in interacting dilute Bose gases. In the first part of the talk we study the coherent flow of interacting Bose-condensed atoms in presence of a single defect or an extended disordered potential. We show that a variation of the condensate velocity v with respect to the defect or disordered potential induces different regimes of quantum transport. At velocities v small compared to the sound velocity c of the condensate the flow shows superfluid behavior, whereas a domain of time dependent flow is reached when v becomes comparable to c. For velocities v considerably larger then the sound velocity a regime of quasi-dissipationless transport is found where the creation of elementary excitations is strongly oppressed. We point out that in this domain, depending of the extent of the disordered region, the system enters an Anderson localized phase. In the second part we consider the experimentally relevant situation where the condensate oscillates in a shallow harmonic trap to which a small defect- or disorder- potential is superimposed. We obtain a global picture characterizing the dynamical properties of the dipole oscillations (e.g. damping of the oscillations), where we can recover the different regimes of quantum transport presented in the first part of the talk. We discuss our findings in the context of recent experiments [1,2,3] and address the question under which circumstances Anderson localization is of relevance for these systems.

[1] C. Fort et al., Phys. Rev. Lett. 95, 170410 (2005)
[2] J. E. Lye et al., Phys. Rev. A 75, 061603 (2007)
[3] P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)

• 5 Dec 2007 - Michael M. Wolf (MPQ München)
Entanglement based tools for Quantum Many-Body Physics
The talk will address recent attempts of applying tools and insights from Quantum Information Theory in Quantum Many-Body Physics. Motivated by entropic area laws we will discuss powerful entanglement based representations of quantum many-body states - so called MPS/PEPS representations. These lead to both, novel analytic results (on solvable models, quantum phase transitions, RG flows, etc) and new numerical simulation methods beyond DMRG and Monte Carlo techniques.

• 27 Nov 2007 - Axel Maas (Bratislava) 16:15 hrs @ SR Pw 16
Gluons at finite temperature
Gluons are not part of the physical spectrum at zero temperature. It is a natural question to ask, whether this is changed after a phase transition which occurs when heating up a system of gluons. Results on this question from lattice gauge theory and functional methods will be presented. These indicate that gluons are never part of the physical spectrum, not even at large or asymptotically high temperatures.

• 21 Nov 2007 - Thomas Gasenzer (Heidelberg)
(together with Kalter-Quanten-Kaffee-Seminar)
Functional renormalisation group approach to far-from-equilibrium quantum field dynamics

• 7 Nov 2007 - Prof. Y. Igarashi (Niigata University)
Quantum Master Equation for Yang-Mills theory in ERG
We discuss a general method to derive the Ward-Takahashi identity for the Wilson action for gauge theories, especially for Yang-Mills theory, in ERG. The identity makes it possible to realize a gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the nilpotency of the BRS transformation is lost. We apply the Batalin-Vilkovisky antifield formalism to lift the Ward-Takahashi identity to a quantum master equation. The extended BRS transformation regains nilpotency.

## SS 2007

• 21 Sep 2007 - Alexander Branschädel (Heidelberg) 14:15 hrs @ SR Pw 16
Transport equations for an ultracold Bose gas

• 10 Jul 2007 - Falk Bruckmann (Regensburg) 14:15 hrs @ SR Pw 16
Instanton constituents in sigma models and Yang-Mills theory

• 8 Jun 2007 - Daniel Spielmann (Tuebingen) 14:15 hrs @ SR Pw 16
On confinement in Sp(2) lattice gauge theory

• 1 Jun 2007 - Cedric Bodet (Mons) 14:15 hrs @ SR Pw 16
Heavy tetraquark stability
Jim Kallarckal (Aachen)
Lepton flavor violating processes in quantum field theory

• 10 May 2007 - Markus Oberthaler (Heidelberg) 16:15 hrs @ SR Pw 16
title tba
(Teilchentee)

• 3 May 2007 - Dieter Heermann (Heidelberg) 14:15 hrs @ SR Pw 19
A new class of random matrices
(Seminar zur Theorie komplexer Systeme)

• 26 Apr 2007 - Manfred Bohn (Heidelberg) 14:15 hrs @ SR Pw 19
A model for polymers with loops
(Seminar zur Theorie komplexer Systeme)

• 20 Apr 2007 - Michael Fromm (Tübingen) 15:00 hrs @ SR Pw 19!
SU(2) projection of SU(3)
Assuming that certain classes of gauge field configurations, lying in subalgebras of the Lie gauge group's Lie algebra, are the relevant degrees of freedom (dof) for confinement, the corresponding subgroups of the gauge group are directly accessed with lattice gauge theory: As happened before within the Dual Superconductor model (U(1)^(N-1)) investigations or alternatively within the Center Vortex picture (Z_N) access is achieved via gauge fixing and subsequent gauge projection. Leaving a remnant symmetry, the degrees of freedom of the symmetry left are then investigated as for their confining behaviour. Aim of this work was the application to SU(3), the subgroup being a SU(2) in "spin s = 1" representation.

## Other seminars at the Institute for Theoretical Physics

 University Faculty Institute