Numerical Verification of the Fluctuation-Dissipation Theorem for Isolated Quantum Systems.

摘要: The fluctuation-dissipation theorem (FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address question whether FDT obeyed by isolated quantum an energy eigenstate. In framework eigenstate thermalization hypothesis, we derive formal expression for two-time correlation functions eigenstates or diagonal ensemble. They satisfy Kubo-Martin-Schwinger condition, which sufficient and necessary condition FDT, infinite system size limit. also obtain finite correction to finite-sized systems. With extensive numerical works $XXZ$ spin chain model, confirm our theory correction. Our results can serve as guide line experimental study on system.