Probing many-body systems near spectral degeneracies

TL;DR

This paper introduces a method using diagonal elements of the time correlation matrix to analyze quantum systems, revealing how spectral degeneracies and symmetry breaking influence quantum evolution and decay rates, demonstrated in a bosonic Josephson junction.

Contribution

It presents a novel approach to probe many-body quantum systems near spectral degeneracies using time correlation matrices, highlighting effects of degeneracies on decay dynamics.

Findings

Spectral degeneracies cause divergence in decay rates.

The method distinguishes recurrent and decaying parts of quantum evolution.

Application to a bosonic Josephson junction reveals localization transition.

Abstract

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.