Quantum Violation of Fluctuation-Dissipation Theorem

TL;DR

This paper demonstrates that the fluctuation-dissipation theorem is partially violated in quantum systems during equilibrium fluctuation measurements, revealing a genuine quantum effect that persists macroscopically, and introduces the concept of a squeezed equilibrium state.

Contribution

The study reveals the partial violation of the fluctuation-dissipation theorem in quantum systems and introduces the concept of a squeezed equilibrium state during measurements.

Findings

Quantum fluctuation-dissipation theorem is partially violated.

Measurement induces a squeezed equilibrium state.

Macroscopic quantum effects persist in equilibrium fluctuations.

Abstract

We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a `squeezed equilibrium state,' which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.