Measuring lifetime of correspondence with classical decay of correlation in quantum chaos

TL;DR

This paper introduces a method using a weakly coupled linear oscillator to measure the lifetime of decay of correlation in quantum chaotic systems, revealing lifetimes often exceed the Heisenberg time and depend on superposition states.

Contribution

It proposes a novel detector setup for observing time-irreversible behavior in quantum chaos and characterizes the lifetime of correlation decay beyond traditional limits.

Findings

Lifetime exceeds Heisenberg time in general cases.

Lifetime scales with the product of Hilbert space dimension and superposed eigenstates.

In full superposition, lifetime scales as the square of the Hilbert space dimension.

Abstract

A very weakly coupled linear oscillator is proposed as a detector for observing time-irreversible characteristics of a quantum system, and it is used to measure the lifetime during which a classically chaotic quantum system shows decay of correlation. Except for a particular case where the lifetime agrees with the conventional Heisenberg time, which is proportional to the Hilbert space dimension $N$, it is in general much longer: the lifetime increases in proportion to the product of $N$ and the number of superposed eigenstates, and is proportional to $N^2$ in the case of full superposition.