Thermal Fluctuations in Quantized Chaotic Systems

Mark Srednicki

doi:10.1088/0305-4470/29/4/003

paper

Thermal Fluctuations in Quantized Chaotic Systems

arXiv:chao-dyn/9511001 · doi:10.1088/0305-4470/29/4/003

Abstract

We consider a quantum system with $N$ degrees of freedom which is classically chaotic. When $N$ is large, and both $ℏ$ and the quantum energy uncertainty $Δ E$ are small, quantum chaos theory can be used to demonstrate the following results: (1) given a generic observable $A$ , the infinite time average $A$ of the quantum expectation value $< A (t) >$ is independent of all aspects of the initial state other than the total energy, and equal to an appropriate thermal average of $A$ ; (2) the time variations of $< A (t) > - A$ are too small to represent thermal fluctuations; (3) however, the time variations of $< A^{2} (t) > - < A (t) >^{2}$ can be consistently interpreted as thermal fluctuations, even though these same time variations would be called quantum fluctuations when $N$ is small.

6 pages in RevTeX 3.0, this version to be published in J.Phys.A

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Semiclassical form factor of matrix element fluctuations

Thermal Fluctuations in Quantized Chaotic Systems

Abstract

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