New Equilibrium Ensembles for Isolated Quantum Systems.

Fabio Anza

doi:10.3390/e20100744

Abstract

The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called “diagonal ensemble” . Building on the intuition provided by Jaynes’ maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to . As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the “thermal ansatz” of Gibbs ensembles.

Highlights

The theory of Statistical mechanics is meant to address the equilibrium physics of macroscopic systems
Maximum Entropy Principle [46,47], we develop a novel technique to generate progressively better approximations to the equilibrium state of an isolated quantum system
There is a simple connection between ρDE and Jaynes’ Maximum Entropy Principle

Summary

Introduction

The theory of Statistical mechanics is meant to address the equilibrium physics of macroscopic systems Both at the classical and at the quantum level, the whole theory is based on the thermal equilibrium assumption. Statistical Mechanics is able to describe equilibrium phenomena even in small isolated quantum systems [11] This points towards an “early emergence” of the thermal equilibrium assumption, already for systems of modest sizes. Maximum Entropy Principle [46,47], we develop a novel technique to generate progressively better approximations to the equilibrium state of an isolated quantum system Using this perspective, the Canonical Gibbs Ensemble is understood as the first-level of a hierarchical set of ensembles which. We are interested in developing a theory for isolated quantum systems at equilibrium which goes beyond the thermal assumption. We ask: How does the picture change when both quantum effects and system-size-dependent fluctuations are not negligible? Our framework can be used to answer this and similar questions

Isolated Quantum Systems

Results

Meaning of the Approximation

Examples

Summary and Conclusions