Quantitative probing of quantum-classical transition for the arrival time distribution

TL;DR

This paper investigates how quantum arrival time distributions transition to classical results as mass increases, providing a quantitative framework for understanding the quantum-classical boundary.

Contribution

It introduces a scheme to quantitatively study the emergence of quantum-classical agreement, specifically applied to quantum arrival time distributions in a linear potential.

Findings

Quantum arrival time distributions approach classical results with increasing mass.

The scheme quantitatively characterizes the quantum-classical transition.

Results are demonstrated for Gaussian wave packets in linear potentials.

Abstract

The classical limit problem of quantum mechanics is revisited on the basis of a scheme that enables a quantitative study of the way the quantum-classical agreement emerges while going through the intermediate mass range between the microscopic and the macroscopic domains. As a specific application of such a scheme, we investigate the classical limit of a quantum time distribution - an area of study that has remained largely unexplored. For this purpose, we focus on the arrival time distribution in order to examine the way the observable results pertaining to the quantum arrival time distribution which is defined in terms of the probability current density gradually approach the relevant classical statistical results for an ensemble that corresponds to a Gaussian wave packet evolving in a linear potential.