The black hole complementarity principle is a conjectured solution to the black hole information loss paradox. In this talk, we will explore how the complementarity principle can emerge in a way that is consistent with quantum information theory via explicit microscopic models that preserve unitarity and a local semi-classical description of the black hole horizon. In particular, we will consider simple toy models where simple quantum systems are coupled to a black hole and show how the initial state of the quantum system is encoded both into the late-time quantum trajectory of the quantum system as well as the late-time (non-linear) ringdown of the black hole. Such models provide insights into how information can be encoded in the interior and exterior of black holes without encountering paradoxes.

# Elizaveta Safonova: Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density P(I) for the single-point intensity I decays as a powerlaw for large intensities: P(I) ∼ I −(M+2), provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law P(I) ∼ exp(−I/I) which turns out to be valid only in the limit M → ∞. We also find the joint probability density of intensities I1, . . . , IL in L > 1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For L → ∞ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

# Sergej Moroz: Quantum dynamics at a Kramers-Wannier dual interface

I will present our on-going work on quantum time evolution after a local quench at an interface between paramagnetic and ferromagnetic regions of a transverse field Isingmodel. The two regions are related by the Kramers-Wannier duality and thus support elementary excitations with the same energy dispersion but different physical nature. For open chain geometry a novel symmetry appears, a combination of the Kramers-Wannier transformation and a reflection, which squares to the Ising Z_2 symmetry. I will also present our first numerical results of time evolution at the interface.

# Ryan Weller: Fun with large N

Large-*N* quantum field theories are a playground for doing non-perturbative physics. Certain large-*N* theories turn out to be asymptotically free in *d*=4 and have features like bound states, just like quantum chromodynamics (QCD) and Yang–Mills theories. Their asymptotic freedom is connected to their apparent non-Hermiticity. However, when coupled with an antilinear symmetry, in many cases referred to as *PT* symmetry, this non-Hermicity does not prevent such theories from having real, bounded spectra and a notion of unitarity. It’s possible to calculate equations of state, phase diagrams, and transport coefficients like shear viscosity *η*/*s* in these theories. I will talk in particular about the O(*N*) model, which is relevant to Higgs physics when *N*=4. I’ll discuss the phase structure at large *N*. There is a first-order phase transition at finite temperature, which has implications for cosmology. In particular, the stable vacuum is *not* the spontaneous symmetry broken (SSB) vacuum, as is otherwise assumed in the Standard Model of particle physics. I’ll demonstrate how one can generate “mass from nothing”, without SSB, when a massless Higgs field is coupled to a U(1) Abelian gauge field. Lastly, I’ll briefly talk about how large-*N* techniques in the O(*N*) model are analogous to a method for non-perturbative analytical calculations in QCD and Yang–Mills theories, via so-called R*n* resummation methods. This analogy might allow a study of the phase structure, transport coefficients, and confinement in QCD and Yang–Mills, with applications to the quark–gluon plasma and neutron stars.

# Lluis Masanes: Conformal quantum circuits and holography

We introduce a spin-chain model with dynamics consisting of a unitary circuit with discrete conformal symmetry. This model is holographically dual to a toy theory of quantum gravity in 2+1 dimensions, where certain tensor-network states correspond to classical discrete geometries. Unlike previous approaches, like holographic codes, these tensor networks and geometries evolve in time, reproducing some phenomena from general relativity. Also, these states satisfy the Ryu-Takayanagi correspondence between entanglement and geometry, but they provide much more, they contain a complete description of the bulk, including the interior of black holes, a feature that is not so transparent in standard AdS/CFT.

# Alexander Soloviev: Spectra and transport in the RTA

I will discuss the kinetic Boltzmann equation in the relaxation time approximation (RTA), a simple way to analytically obtain information of collective real-time transport. I will present the analytically computed retarded two-point Green’s functions of conserved operators in thermal states at non-zero density, and in the absence/presence of broken translational symmetry. This naturally leads to a discussion of the analytic structure and the transport properties such correlators imply. Looking forward, I will go beyond the usual standard truncation scheme used to close the BBGKY heirarchy and how such modifications lead to novel complex structure.

# Davide Fioravanti: Exploring gauge theories — maybe BHs — with Floquet and Painlevé

We show how functional relations, which can be considered as a definition of a quantum integrable theory, entail an integral equation that can be extended upon introducing dynamical variables to a Marchenko-like equation. Then, we naturally derive from the latter a classical Lax pair problem. We exemplify our method by focusing on the massive/massless version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence involving the sinh-Gordon/Lioville model, first emerged in the gauge theories and scattering amplitudes/Wilson loops AdS3 context with many moduli/masses, but in a way which reveals its generality. In fact, we give some hints, in the end, to its application to spin chains.

# Ana Retore: Constructing integrable long range deformations of spin chains

*Ana Retore, Durham University (UK)*

# Igor Poboiko: Selected topics in quantum mechanics

*This mini-course will cover several selected topics in quantum mechanics. The first part will be focusing on adiabatic approximation and, including both non-stationary and stationary counterparts, latter also known as Born-Oppenheimer approximation. In the second part we will discuss the extension of the WKB semiclassical approximation to the complex plane, focusing on Stokes phenomenon, and apply it to the problem of over-the-barrier semiclassical reflection, linking it to the transition probability in the stationary adiabatic approximation. The third part will be focusing in great detail on the quantum tunneling problems in the path integral approach, including calculation of the functional determinants governing the behavior of pre-exponential factors by means of the Gelfand-Yaglom formalism. The last part will be devoted to the analysis of the one-dimensional Anderson localization using the Dorokhov-Mello-Pereyra-Kumar (DMPK) formalism.*

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All lectures will take place in the seminar room 133 (Jadranska Ulica 21, new building). The schedule is

# 11th Trieste-Ljubljana-Zagreb Meeting in Statistical Physics and Condensed Matter

Please find the program of the 11th Trieste-Ljubljana-Zagreb meeting