Quantum Violation of Fluctuation-Dissipation Theorem

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.

version 3: fixed typos. 30 pages, 6 figures. A paper for an invited talk at STATPHYS26, Lyon, France, 2016

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• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Macroscopic Quantum Violation of Fluctuation-Dissipation Theorem in Equilibrium
• Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems
• Key Observable for Linear Thermalization
• Onsager's regression hypothesis adjusted to quantum systems
• Out-of-equilibrium fluctuation-dissipation relations verified by the electrical and thermoelectrical ac-conductances in a quantum dot
• Robustness of equilibrium off-diagonal current fluctuation against localization of electron states in macroscopic two-dimensional systems
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Backaction-free measurement of quantum correlations via quantum time-domain interferometry