Control of fluctuations and heavy tails for heat variation in the two-time measurement framework

TL;DR

This paper investigates heat fluctuations in quantum systems within the two-time measurement framework, establishing conditions for bounded moments and analyticity, and demonstrating the emergence of heavy tails when these conditions are not met.

Contribution

It provides sufficient ultraviolet regularity conditions ensuring bounded heat moments and analyticity, and shows these conditions are necessary through canonical examples.

Findings

Bounded perturbations lead to uniformly bounded heat moments.

Failure of ultraviolet conditions results in heavy tails in heat distribution.

Heavy tails can prevent the existence of higher moments like the fourth moment.

Abstract

We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0. On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation.