08:45  09:00

Frank Jülicher (Director MPIPKS) & Scientific Coordinators
Opening


Chair: Stefan Kehrein

09:00  09:35

Olivier Giraud
(LPTMS Orsay)
Probing symmetries of quantum manybody systems through ratio statistics
The idea of describing properties of complicated systems, such as complex atomic nuclei, using random numbers dates back to the 1950s. One application is in quantum mechanics, where random numbers are a tool for making accurate predictions about the statistics of discrete energy levels a system can assume. More precisely, the statistical distribution of the spacings between successive energy levels can be compared with distributions from random matrices, which provides a signature of whether the system behaves in a regular or a chaotic way. Random matrix theory (RMT) has since grown into an active branch between mathematics and physics, and has found applications in many branches of physics but also in biology or finance.
Analyzing universal statistical properties of a spectrum requires unfolding. Unfortunately, this can lead to spurious results: for manybody systems, the density of states is generically far from being uniform, which makes the use of the unfolding procedure rather inaccurate. This is why in recent years the focus has shifted away from the statistics of energy spacings to the statistics of ratios between successive spacings. This ratio statistics is by now a widely used tool of quantum chaos, that allows to compare experimental or numerical observations with theoretical predictions.
However, extra symmetries of the system, which may be hidden, can split the spectrum into independent random blocks, and thus modify these statistics. We show that it is possible to extend the theory of spacing ratio statistics to account for the presence of additional symmetries. Our results allow to probe for the existence of symmetries if they were unknown. We derive analytical surmises for random matrices with independent block structure, and illustrate our approach on a number of applications from manybody physics. This provides a tool not only to get a signature of chaos or regularity in systems with symmetries, but also to uncover these symmetries if they were previously unnoticed.

09:35  10:10

Yan Fyodorov
(King's College London)
Resonances in wave reflection from a disordered medium: nonlinear σmodel approach
We develop a general nonperturbative characterisation of universal features of the density $\rho(\Gamma)$ of Smatrix poles (resonances) $E_n − i\Gamma_n$ describing waves incident and reflected from a disordered
medium via a single Mchannel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several
instances of systems with broken timereversal invariance, in particular for quasi1D medium as well as for Random Regular Graph. In the case of perfectly coupled lead with $M \sim 1$ the most
salient features are tails $\rho(\Gamma)\sim 1/\Gamma$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim 1/\Gamma^2$
for broad resonances reflecting states located in the vicinity of the attached wire. For multimode wires with $M\gg 1$ intermediate asymptotics $\rho(\Gamma)\sim 1/\Gamma^{3/2}$ is shown to emerge, reflecting diffusive nature of decay into wide enough contacts. The presentation will be based on a joint work with M. Skvortsov and K. Tikhonov.

10:10  11:05

coffee break & discussions

11:05  11:40

Ben Freivogel
(University of Amsterdam)
Computing quantum gravity effects with wormholes
The longtime correlation function is a wellknown probe of information loss in black holes. I will show how the magnitude of the longtime correlator, averaged over a family of states, can be computed in gravity. This work extends recent progress in understanding corrections to semiclassical gravity to situations where an average over theories is not available, and to a wider class of observables. Based on https://arxiv.org/abs/2105.12771 and work in progress.

11:40  12:15

Eugene Kanzieper
(Holon Institute of Technology)
Power spectrum of the circular unitary ensemble
We study the power spectrum of eigenangles of random matrices drawn from the circular unitary ensemble $({\rm CUE})$ and show that it can be evaluated in terms of either a Fredholm determinant, or a Toeplitz determinant, or a sixth Painlev\'e function. In the limit of infinitedimensional matrices, we derive a {\it concise} parameterfree formula for the power spectrum which involves a fifth Painlev\'e transcendent. Further, we discuss a universality of the predicted power spectrum law (in randommatrixtheory context and beyond), and present a fair evidence that a universal Painlevé V curve is observed in the power spectrum of nontrivial zeros of the Riemann zeta function.

12:15  13:30

lunch & discussions


Chair: Micha Berkooz

15:00  15:35

Stefan Kehrein
(GeorgAugustUniversität Göttingen)
Scrambling and tripartite information in manybody localized systems
The tripartite information is an observableindependent measure for scrambling and delocalization of information. Therefore it is a good observableindependent indicator for distinguishing between manybody localized and delocalized regimes, which we confirm for the XXZchain in a random field. Specifically, we find that the tripartite information signal spreads inside a lightcone that only grows logarithmically in time in the manybody localized regime similar to the entanglement entropy. We also find that the tripartite information eventually reaches a plateau with an asymptotic value that is suppressed by strong disorder.
N. Boelter and S. Kehrein, Phys. Rev. B 105 (2022) 104202

15:35  16:10

Thomas Mertens
(University of Gent)
Chaos and integrability in lowerdimensional gravitational models
In this talk I will discuss manifestations of chaotic behavior in the solvable 2d JT gravity model. Boundary operators in this model are divided into two classes: generic operators that lead to chaotic behavior in outoftime ordered correlators, and special "degenerate" operators that correspond to an integrable subsector of the model and that are related to the embedding of JT gravity within string theory (minimal string).

16:10  16:40

coffee break

16:40  17:15

Sašo Grozdanov
(U. Edinburgh and U. Ljubljana)
Bounds on transport and quantum chaos
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed either for classes of theories or universally for all theories. Few are inviolable. On the other hand, the inequalities recently derived for the growth rate of quantum chaos do appear to be exact and universal. In this talk, I will first review a few of the more influential bounds on transport from past decades and then discuss the ingredients that enter into proofs of bounds on quantum chaos: exponential (Lyapunov) and weak quantum chaos. I will then present a set of new methods for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. At least in systems with holographic duals, these methods allow to make a precise relation between rigorous bounds on transport and a property of quantum chaos known as poleskipping.

18:00  19:00

dinner

19:00

informal discussions
