Assessing Quantum Thermalization in Physical and Configuration Spaces via Many-Body Weak Values

TL;DR

This paper investigates the quantum origin of the arrow of time using weak values in configuration space, revealing how thermalization differs between physical and configuration spaces and providing testable laboratory predictions.

Contribution

It introduces a novel explanation for quantum thermalization and the arrow of time based on weak values and configuration space analysis, highlighting differences from traditional eigenstate thermalization hypothesis.

Findings

Weak values can show nonthermalized behavior despite thermal ensemble expectations.

Thermalization is linked to properties in physical space, not configuration space.

Laboratory tests of many-body weak values can validate the theoretical insights.

Abstract

We explore the origin of the arrow of time in an isolated quantum system described by the Schroedinger equation. We provide an explanation from weak values in the configuration space, which are understood as operational properties obtained in the laboratory following a well-defined protocol. We show that quantum systems satisfying the eigenstate thermalization hypothesis can simultaneously provide thermalized ensemble expectation values and nonthermalized weak values of the momentum, both from the same operational probability distribution. The reason why weak values of the momentum may escape from the eigenstate thermalization hypothesis is because they are linked only to off-diagonal elements of the density matrix in the energy representation. For indistinguishable particles, however, operational properties can not be defined in the configuration space. Therefore, we state that the origin of the arrow of time in isolated quantum systems described by the Schroedinger equation comes from dealing with properties obtained by averaging (tracing out) some degrees of freedom of the configuration space. We then argue that thermalization does not occur in the properties defined in the configuration space, and our argument is compatible with defending that thermalization is a real phenomenon in the properties defined in the physical space. All of these conclusions are testable in the laboratory through many-body weak values.