Quantum Violation of Fluctuation-Dissipation Theorem

Akira Shimizu, Kyota Fujikura

Published 2016-10-11Version 1

We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem is partially violated in quantum systems, as a relation between observed quantities, even if measurements are made in an ideal way that mimics classical ideal measurements as closely as possible. This is a genuine quantum effect, which 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.