Thermal evolution of hole dynamics in the large-dimensional model

David E. Logan, M. P. H Stumpf

We discuss the dynamics of a single hole in t - J model at finite temperature, in the limit of large spatial dimensions. The problem is shown to yield a simple and physically transparent solution, that exemplifies the continuous thermal evolution of the underlying string picture from the T = 0 string-pinned limit through to the paramagnetic phase.

M. Brunner, Fakher F. Assaad, A. Muramatsu

Indrani Bose, Saurabh Gayen

Javier M. Magán

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large- $$ \mathcal{N} $$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large- $$ \mathcal{N} $$ matrix models, where we provide a gauge invariant entanglement entropy for ‘generalized free fields’, again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.

Andrey R. Kolovsky, Dima L. Shepelyansky

We study numerically a model of quantum dot with interacting fermions.At strong interactions with small conductance the model is reduced to the Sachdev-Ye-Kitaev black-hole model while at weak interactions and large conductance it describes a Landau-Fermi liquid in a regime of quantum chaos.We show that above the Åberg threshold for interactions there is an onset of dynamical themalization with the Fermi-Dirac distribution describing the eigenstates of an isolated dot.At strong interactions in the isolated black-hole regime there is also the onset of dynamical thermalization with the entropy described by the quantum Gibbs distribution.This dynamical thermalization takes place in an isolated system without any contact with a thermostat.We discuss the possible realization of these regimes with quantum dots of 2D electrons and cold ions in optical lattices.

Ippei Doi, Kazuhiro Sano, Ken'ichi Takano