Seminar on the Theory of Complex Systems  Summer Term 2019

• Thursday 16.05.2019   at 14 c.t.
  Koenraad Schalm, University of Leiden
  Quantum Chaos, hydrodynamics and black hole scrambling
  

  For perturbative scalar field theories, the late-time-limit of the out-of-time-ordered correlation function that measures (quantum) chaos is shown to be equal to a Boltzmann-type kinetic equation that measures the total gross (instead of net) particle exchange between phase space cells, weighted by a function of energy. This derivation gives a concrete form to numerous attempts to derive chaotic many-body dynamics from ad hoc kinetic equations. As in conventional Boltzmann transport, which follows from the dynamics of the net particle number density exchange, the kernel of this kinetic integral equation is also set by the 2-to-2 scattering rate. This provides a mathematically precise statement of the known fact that in dilute weakly coupled gases late-time transport and early-time scrambling (or ergodicity) are controlled by the same physics. Surprisingly infinitely strongly coupled, large-Nc theories with a holographic dual also possess this relation between early- and late-time physics. The gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. At a special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This pole-skipping point encodes the Lyapunov exponent of quantum chaos.

• Thursday 23.05.2019   at 14 c.t.
  Thomas Barthel, Duke University
  Fundamental limitations for measurements in quantum many-body systems
  

  Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently if we have access to a certain set of experimentally realizable measurements and can extend it through time evolution. For the latter, two scenarios are considered (a) evolution according to unitary circuits and (b) evolution due to Hamiltonians that we can control in a time-dependent fashion. We find that the time needed to realize a certain measurement to a predefined accuracy scales in general exponentially with the system size - posing a fundamental limitation. The argument is based on the construction of epsilon- packings for manifolds of observables with identical spectra and a comparison of their cardinalities to those of epsilon-coverings for quantum circuits and unitary time-evolution operators. The former is related to the study of Grassmann manifolds. The results show that it is a question of clever design to allow for the measurement of observables of interest through efficient dynamical schemes and a suitable encoding of models in quantum simulation protocols. [T. Barthel and J. Lu, Phys. Rev. Lett. 121, 080406 (2018)]

• Thursday 13.06.2019   at 14 c.t.
  Mario Nicodemi, University of Napoli
  Polymer physics of chromosome architecture
  

• Thursday 04.07.2019   at 14 c.t.
  Giacomo Gori (Universita di Padova)
  Geometry of Bounded Critical Phenomena
  

  "What would you do if you were a system at criticality confined in a bounded domain? Of course you would forget about details of the interaction, lattice spacing flowing to an RG fixed point. Besides attaining this bulk universal behavior you would also try (boundary condition permitting) to forget about the confinement becoming "as uniform as possible". Implementing this requirement in absolute geometric language, the one used by general relativity, we obtain novel predictions for the structure of one- and two-point correlators. These predictions are tested successfully against numerical experiments yielding a precise estimate of a critical exponent of the Ising model in three dimensions."

Confirmed for the Winter Term 2019/20: