Classical and Quantum Transport Through Entropic Barriers Modelled by Hardwall Hyperboloidal Constrictions

TL;DR

This paper investigates quantum and classical transport through hyperboloidal constrictions, revealing how geometry influences transmission probabilities and resonances, and offering insights applicable to more complex, non-separable systems.

Contribution

It provides a detailed analysis of quantum and classical transport in hyperboloidal geometries, highlighting the role of phase space structures and separability in entropic barrier dynamics.

Findings

Quantum transmission probabilities are computed and linked to classical phase structures.

Classical and quantum resonances are characterized and related.

Insights into non-separable systems are suggested based on separable models.

Abstract

We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrodinger equation and the classical equations of motion for these geometries we study in detail the quantum transmission probabilities and the associated quantum resonances, and relate them to the classical phase structures which govern the transport through the constrictions. These classical phase structures are compared to the analogous structures which, as has been shown only recently, govern reaction type dynamics in smooth systems. Although the systems studied in this paper are special due their separability they can be taken as a guide to study entropic barriers resulting from constriction geometries that lead to non-separable dynamics.