Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer

TL;DR

This paper proposes a method to assign an internal temperature to small quantum chaotic systems using a microscopic two-level probe, demonstrating that the temperature is well-defined and robust against various coupling and initial conditions.

Contribution

A novel approach using a microscopic thermometer to determine the internal temperature of quantum chaotic systems, showing its independence from probe details.

Findings

Temperature is insensitive to probe-system coupling variations.

The measured temperature aligns with Boltzmann temperature.

Method applicable to small quantum chaotic systems.

Abstract

The extent to which a temperature can be appropriately assigned to a small quantum system, as an internal property but not as a property of any large environment, is still an open problem. In this paper, a method is proposed for solving this problem, by which a studied system is coupled to a two-level system (probe) as a microscopic thermometer. For small quantum chaotic systems, we show that a temperature can be determined, the value of which is sensitive to neither the form, location, and strength of the probe-system coupling, nor the Hamiltonian and initial state of the probe. This temperature turns out to have the form of Boltzmann temperature.