Hilbert-space localization in closed quantum systems

TL;DR

This paper introduces a unifying framework for understanding quantum localization in closed systems, extending semiclassical ideas and analyzing how initial states and interactions influence localization.

Contribution

It presents a general phase-space perspective on Hilbert-space localization and introduces a recursive projection method to study its dependence on initial conditions and interaction strength.

Findings

Localization measure varies with initial state

Interaction strength affects localization

Recursive projection method effectively analyzes localization

Abstract

Quantum localization within an energy-shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space "Anderson localization" and its many-body Fock-space version. We use the term "Hilbert-space localization" in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the Bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state, and on the strength of the many-body interactions using a novel recursive projection method.