On the selection of the classical limit for potentials with BV derivatives

TL;DR

This paper investigates how to accurately derive the classical limit of quantum evolution for wave packets near singular trajectories, especially in cases with rough potentials having BV derivatives, establishing conditions for correct classical limit selection.

Contribution

It demonstrates that even with BV vector fields, the classical limit can be correctly selected under certain conditions, extending understanding of quantum-classical correspondence in rough potential scenarios.

Findings

Classical limit can be correctly selected with BV derivatives.

Conditions identified for accurate classical limit in rough potentials.

Extension of classical limit theory to BV vector fields.

Abstract

We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.