# Tilman Enss | Teaching in previous semesters

## Many-body physics with ultracold atoms (MVSeminar)

#### Winter term 2015/16

**This theory seminar introduces key questions and concepts in the
fast-evolving field of ultracold atomic gases.**

Supervisor: Priv.-Doz. Dr. Tilman Enss

general objectives of advanced mandatory
seminars (page 18)

Fri 9.15-11.00h, Philosophenweg 19, SR [LSF]

#### Seminar Topics

**2015-10-30: Scattering of ultracold atoms and Feshbach resonances**

low-energy scattering can be characterized by an s-wave scattering length, which diverges at a Feshbach resonance, leading to strong interactions; this is described by single- and two-channel models

*Ketterle, ch. 4.1-4.2, parts of 5; Bloch/Dalibard/Zwerger, ch. I; Dalibard*

**2015-11-06: Bose-Einstein condensates and Bogoliubov theory**

many bosons can condense into a single quantum state to form a BEC; excitations in the BEC are described by Bogoliubov theory

*Pitaevskii, ch. 2, 4, 6.1-6.2*

**2015-11-13: Vortices in rotating Bose-Einstein condensates**

the dynamics of a BEC can be described by the Gross-Pitaevskii equation, which admits vortex solutions in a rotating BEC

*Pitaevskii, ch. 5*

**2015-11-27: Bose-Hubbard model and the Mott insulator transition**

with bosonic atoms in an optical lattice one can realize a Bose-Hubbard model, which exhibits a phase transition between a Mott insulator and a superfluid state

*Bloch/Dalibard/Zwerger, ch. IV; Diehl p. 138-172 (in particular 148-160, 168-172); (Jaksch)*

**2015-12-04: The BCS-BEC crossover and universal thermodynamics**

the interacting Fermi gas exhibits a smooth crossover from a weakly attractive BCS superfluid through the strongly interacting unitary regime to a weakly repulsive Bose-Einstein condensate of molecules

*Zwerger, ch. 3 (by Heiselberg); Ketterle, ch. 4.3++; Bloch/Dalibard/Zwerger, ch. VIII*

**2015-12-11: Fermi polarons, variational wavefunction and polaron-to-molecule transition**

a mobile impurity in a Fermi sea can bind into a molecule at strong attraction

*Chevy; Punk; Kohstall*

**2015-12-18: Kosterlitz-Thouless transition in two-dimensional systems**

in two dimensions, quantum fluctuations can be so strong that they destroy long-range order, but superfluidity is still possible

*Pitaevskii 6.7, 17.5; (Cardy 6.2, 6.4?)*

**2016-01-08: Nonequilibrium dynamics and integrability**

while a system brought out of equilibrium usually thermalizes, in one dimension there can be so many conservation laws that it keeps a memory of its initial state

*Kinoshita; Rigol; Polkovnikov, ch. III*

**2016-01-15: Transport in cold gases and perfect fluidity**

as quantum fluids are made strongly interacting, their friction (viscosity) is reduced; remarkably, there appears to be a universal minimum value for the viscosity in very different physical systems which characterizes perfect fluids

*parts of Schaefer*

#### Literature

- Bloch, Dalibard, and Nascimbene, Nature Phys. 8, 267 (2012)
- Bloch, Dalibard, and Zwerger, Rev. Mod. Phys. 80, 885 (2008)
- Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Univ. Press (1996)
- Chevy, Phys. Rev. A 74, 063628 (2006)
- Dalibard, Varenna lecture notes (1998)
- Diehl, Innsbruck lecture notes (2013)
- Enss, Condensed Matter Theory lecture notes (2015) (for participants only)
- Feynman, Int. J. Theor. Phys. 21, 467 (1982)
- Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)
- Ketterle and Zwierlein, Varenna lecture notes (2008)
- Kinoshita, Wenger, and Weiss, Nature 440, 900 (2006)
- Kohstall et al., Nature 485, 615 (2012)
- Pethick and Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge Univ Press 2008
- Pitaevskii and Stringari, Bose-Einstein Condensation, Clarendon Press 2003
- Polkovnikov et al., Rev. Mod. Phys. 83, 863 (2011)
- Punk, Dumitrescu, and Zwerger, Phys. Rev. A 80, 053605 (2009)
- Rigol, Dunjko, and Olshanii, Nature 452, 854 (2008)
- Schaefer and Teaney, Rep. Prog. Phys. 72, 126001 (2009)
- Zwerger (ed.), The BCS-BEC Crossover and the Unitary Fermi Gas, Springer Lecture Notes in Physics 836 (PDF available from the university library)

#### Prerequisites

- Quantum Mechanics
- Statistical Physics (recommended)
- Condensed Matter Theory (useful)

#### Formalities

- oral presentation max. 60 minutes, followed by discusssion
- hand in writeup until 05 Feb 2016: an essay on your seminar topic, with full sentences, sketches/figures if you like, but not just your slides; max. 15 pages but you are very welcome to make it shorter
- 6 credit points, grade composed of writeup, oral presentation, and participation in discussion
- attendance is mandatory; please send me an email if you cannot come
- it is recommended that we go over your talk together before your presentation; please make an appointment for, say, the Monday before your talk.

## Condensed Matter Theory (MVTheo2)

#### Summer term 2015

This course introduces the concepts and methods of modern condensed matter theory. In the first part, Green's functions and the diagrammatic technique are used to discuss metals, Fermi liquids and superconductors. The second part covers several advanced topics such as Bose-Einstein condensation, quantum phase transitions, and the Kondo effect. The exercises also show how to compute experimental observables.

Description in the course handbook (page 67)

#### Contents

- Introduction
- Fermions, bosons, and second quantization
- Electrons in periodic crystals, band structure
- Green's functions and perturbation theory
- Metals: Jellium model, charge excitations, and phonons
- BCS theory of superconductivity
- Landau Fermi liquid theory, Luttinger liquids
- Bose-Einstein condensation, superfluidity and symmetry breaking
- Magnetism and quantum phase transitions

Lecture Notes (for participants)

#### Dates and Location

Lecture Monday 11.15-13.00h, Philosophenweg 12, kHS [LSF]

and Wednesday 11.15-13.00h, Philosophenweg 12, kHS.

Exercise (Dr. Michael Scherer) Friday 14.00-16.00h, Philosophenweg 12, R106.

Please register for the course at this URL
for notifications and/or for taking part in the exam.

#### Prerequisites

- Quantum Mechanics (PTP4)
- Theoretical Statistical Physics (MKTP1) — recommended

#### Literature

- Ashcroft and Mermin, Solid State Physics
- Tinkham, Introduction to Superconductivity
- Altland and Simons, Condensed Matter Field Theory
- Fetter and Walecka, Quantum Theory of Many-Particle Systems
- Negele and Orland, Quantum Many-Particle Systems

#### Further material

- Anderson, More is different, Science
**177**, 393 (1972) - Sigrist, Lecture notes on Solid State Theory
- Komnik, Lecture notes on Condensed Matter Theory
- for a crash course in statistical physics, see e.g. Fetter/Walecka, ch. 2

#### Exam

Students who do the homework and present their solution during the exercises will be admitted to the written exam. In order to participate in the exam you need to register for the course at this URL. The exam will be held on Wednesday, 22 July 2015, from 11:15-12:45h. The exam will be graded; those who pass will acquire 8 credit points.

## Theory of Ultracold Atoms (MVSeminar)

#### Winter term 2014/15

**The seminar introduces key questions and concepts in the
fast-evolving field of ultracold atomic gases**

Supervisor: PD Dr. Tilman Enss

general objectives of advanced mandatory
seminars (page 18)

Fri 9.15-11.00h, Philosophenweg 19, SR [LSF]

## Condensed Matter Theory (MVTheo2)

#### Summer term 2014

Course record in the university directory (LSF)

Description in the course handbook (page 67)

This course introduces the concepts and methods of modern condensed matter theory. In the first part, Green's functions and the diagrammatic technique are used to discuss metals, Fermi liquids and superconductors. The second part covers several advanced topics such as Bose-Einstein condensation, quantum phase transitions, and the Kondo effect. The exercises also show how to compute experimental observables.

#### Dates and Location

Lecture Monday 11.15-13.00h, Philosophenweg 12, kHS

and Wednesday 11.15-13.00h, Philosophenweg 12, kHS;

Exercise (Laura Classen) Thursday 11.15-13.00h, Philosophenweg 12, R105.

Please register for the course at this URL.

#### Contents

- Introduction
- Fermions, bosons, and second quantization
- Electrons in the periodic crystal, band structure
- Green's functions and perturbation theory
- Metals: Jellium model, charge excitations, and phonons
- Landau Fermi liquid theory, Luttinger liquids
- BCS theory of superconductivity
- Bose-Einstein condensation, superfluidity and symmetry breaking
- Magnetism and quantum phase transitions

#### Prerequisites

- Quantum Mechanics (PTP4)
- Theoretical Statistical Physics (MKTP1) — recommended

#### Literature

- Ashcroft and Mermin, Solid State Physics
- Tinkham, Introduction to Superconductivity
- Altland and Simons, Condensed Matter Field Theory
- Fetter and Walecka, Quantum Theory of Many-Particle Systems
- Negele and Orland, Quantum Many-Particle Systems

#### Further material

- Sigrist, Lecture notes on Solid State Theory
- Komnik, Lecture notes on Condensed Matter Theory
- for a crash course in statistical physics, see e.g. Fetter/Walecka, ch. 2
- literature on Grassmann numbers:
- F. Wegner, Grassmann-Variable, Lecture Notes 1998
- K. Efetov, Adv. Phys.
**32**, 53 (1983) - F. A. Berezin, Introduction to Superanalysis, Reidel Dordrecht 1987

#### Exam

Students who do the homework and present their solution during the exercises will be admitted to the written exam. In order to participate in the exam you need to register for the course at this URL. The exam will be held on Wednesday, 23 July, from 14:15-15:45h. The exam will be graded; those who pass will acquire 8 credit points.

## Spezielle Probleme der Quantenmechanik

#### Wintersemester 2013/2014

Tutor für das Seminar Spezielle Probleme der Quantenmechanik bei Prof. Thomas Gasenzer

## Quantenmechanik

#### Sommersemester 2013

Lecture Assistant für Theoretische Physik PTP4 (Quantenmechanik) bei Prof. Thomas Gasenzer

## Many-body methods in solid state physics (Dr. Tilman Enss)

#### Winter term 2012/2013

Course record in the university directory (LSF)

Course announcement

A system of many interacting particles can behave very differently
from its constituents, *"more is different"* (Anderson). In
this two-hour course the tools of quantum field theory are introduced
(Green's functions, Grassmann algebra, path integrals) and applied to
explain current and illustrative problems in solid state physics
(superfluids, quantum phase transitions and the BCS theory of
superconductivity). The exercises show how to compute experimental
observables.

#### Contents

- Second quantization
- Green's functions
- BCS theory of superconductivity
- Coherent states and path integrals
- Perturbation theory and Wick's theorem, Self-energy and Dyson equation
- Interacting Bose gas, superfluidity and symmetry breaking
- Quantum phase transitions in the transverse Ising model

#### Evaluation

This course has been evaluated by the Fachschaft, which you can ask for the result (sorry I cannot publish it here).#### Problem sets

#### Prerequisites

- Quantum mechanics
- Statistical physics

#### Literature

- Altland und Simons, Condensed Matter Field Theory
- Negele and Orland, Quantum Many-Particle Systems
- Tinkham, Introduction to Superconductivity
- Xiao-Gang Wen, Quantum Field Theory of Many-Body Systems

#### Dates and Location

Lecture Thursday 11.15-13.00h, Philosophenweg 12, kHSExercise Friday 09.15-11.00h, Philosophenweg 12, kHS

#### Credits/Exam

4 credit points can be obtained. An oral exam will be offered at the end of the course.

## Quanten-Vielteilchentheorie (Dr. Tilman Enss)

#### Sommersemester 2012

## Quanten-Vielteilchentheorie (Dr. Tilman Enss)

#### Sommersemester 2011

## Statistische Mechanik und Thermodynamik (Prof. Wilhelm Zwerger)

#### Sommersemester 2010

## Quantenmechanik I (Prof. Wilhelm Zwerger)

#### Sommersemester 2009

## Quantenmechanik II (Prof. Thorsten Feldmann)

#### Wintersemester 2008/2009

## Theoretische Festkörperphysik (Prof. Roland Netz)

#### Sommersemester 2008

#### Vorlesungen über Supraleitung (von Tilman Enss):

Vorlesung 1 (02.07.2008): Fröhlich-Transformation, Cooper-Instabilität

Vorlesung 2 (04.07.2008): BCS-Wellenfunktion, Gap-Gleichung, Bogoliubov-Transformation