Thermally isolated Luttinger liquids with noisy Hamiltonians

TL;DR

This paper investigates energy fluctuations and correlation deviations in a thermally isolated, noisy Luttinger liquid, revealing classical noise dominance and unique scaling behaviors in a driven quantum system.

Contribution

It introduces a method to distinguish classical and quantum energy fluctuations and demonstrates classical noise dominance in a driven Luttinger liquid system.

Findings

Classical noise dominates energy fluctuations in the thermodynamic limit.

Energy fluctuations do not decay with system size, unlike in equilibrium.

Correlation functions exhibit simple scaling deviations from ground state.

Abstract

We study the dynamics of a quantum-coherent thermally isolated Luttinger liquid with noisy Luttinger parameter. To characterize the fluctuations of the absorbed energy in generic noise-driven systems, we first identify two types of energy moments, which can help tease apart the effects of classical (sample-to-sample) and quantum sources of fluctuations. One type of moment captures the total fluctuations due to both sources, while the other one captures the effect of the classical source only. We then demonstrate that in the Luttinger liquid case, the two types of moments agree in the thermodynamic limit, indicating that the classical source dominates. In contrast to equilibrium thermodynamics, in this driven system the relative fluctuations of energy do not decay with the system size. Additionally, we study the deviations of equal-time correlation functions from their ground-state value, and find a simple scaling behavior.