Abstract
As recently manifested [], the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in the non-interacting basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in the description of this process is the width Γ of the local density of states (LDoS) defined by the initially excited state, the number of particles and the interaction strength. In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the LDoS is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation. The analytical expression relating the two entropies is derived phenomenologically and numerically confirmed in a model of bosons with random two-body interaction, as well as in a deterministic model which becomes completely integrable in the continuous limit.
Highlights
The problem of thermalization in isolated quantum systems remains a hot topic in the field of modern statistical mechanics
In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the local density of states (LDoS) is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation
We have studied two different models, the two-body random interaction (TBRI) model with random two-body interaction and the truncated LL model (t-LL) with a finite number of particles in a finite number of momentum states which is originated from the completely integrable Lieb–Liniger model
Summary
Musei 41, 25121 Brescia, Italy 3 Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, I-27100, Pavia, Italy 4 NSCL and Department of Physics and Astronomy, Michigan State University, E Lansing, Michigan 48824-1321, United States of America Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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