Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

TL;DR

This paper demonstrates that non-Hermitian evolution with balanced gain and loss can enhance quantum chaos signatures in spectral form factors, offering a new physical mechanism for spectral filtering in quantum systems.

Contribution

It introduces a novel approach using non-Hermitian dynamics with balanced gain and loss to enhance quantum chaos signatures, supported by models like SYK and random matrices.

Findings

BGL increases the ramp duration in spectral form factors

BGL lowers the dip and plateau values, indicating chaos enhancement

Engineered filter functions optimize chaos enhancement

Abstract

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.