Physics (Internal)

Onset of thermalization in the Hilbert space of isolated many-body systems

This event is part of the Biophysics/Condensed Matter Seminar Series.

We study analytically and numerically the onset of thermalization in isolated quantum systems with interacting Bose and Fermi particles. To do this, we use two models: one is the model of N bosons interacting via two-body random interactions, and the other is the 1D integrable model of N spins-1/2. We show that in both models the thermalization emerges due to strong quantum chaos quantified in terms of chaotic structure of many-body eigenstates. One of the important results is that in the quench dynamics the number of components in the wave function (in the Hilbert space), increases exponentially in time provided the eigenstates are strongly chaotic. We have developed an analytical approach allowing one to show that the time scale of the exponential increase (which is the same as the time scale for a complete thermalization) is proportional to the number of particles. We also studied how the Bose-Einstein distribution in the first model emerges in time, thus demonstrating the creation of quantum correlations in the process of a complete relaxation. We discuss how this process can be described with the use of the Kolmogorov-Sinai entropy for the systems with a well-defined classical limit. The results allow us to suggest a new approach to the problem of quantum-classical correspondence for many-body systems.