Escape Behavior of Quantum Two-Particle Systems with Coulomb Interactions

TL;DR

This paper investigates how two interacting quantum particles escape from a confined region, revealing exponential decay behavior due to Coulomb interactions, contrasting with power-law decay in free particles, and explores effects of quantum statistics and chaos.

Contribution

It demonstrates that Coulomb interactions cause exponential decay in survival probability, contrasting with free particles' power-law decay, and analyzes quantum effects like statistics and chaos.

Findings

Interacting particles exhibit exponential decay in survival probability.

Free particles show power-law decay asymptotically.

Quantum statistics influence escape behavior.

Abstract

Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by the probability of particles remaining in the confined region, i.e. the survival probability, in comparison with one or two free particles. For free-particle systems the survival probability decays asymptotically in power as a function of time. On the other hand, for two-particle systems with Coulomb interactions it shows an exponential decay in time. A difference of escape behaviors between Bosons and Fermions is considered as quantum effects of identical two particles such as the Pauli exclusion principle. The exponential decay in the survival probability of interacting two particles is also discussed in a viewpoint of quantum chaos based on a distribution of energy level spacings.