Dissipative Effects on Quantum Sticking

TL;DR

This paper investigates how dissipative environments influence quantum sticking and reflection at low energies, revealing modified threshold laws and conditions for perfect reflectivity due to infrared divergences.

Contribution

It provides a non-perturbative analysis of dissipative effects on quantum sticking thresholds using variational mean-field theory, highlighting the role of infrared divergences.

Findings

Low energy sticking probability scales as E^{(1+α)/2(1-α)} for neutral particles.

Charged particles exhibit a different threshold scaling, E^{α/2(1-α)}.

Quantum mirrors can exist for charged particles at zero incident energy.

Abstract

Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a non-perturbative expression for the sticking rate. We find that for weak dissipative coupling $\alpha$, the low energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy $E\to 0$ behaves asymptotically as ${\it s}\sim E^{(1+\alpha)/2(1-\alpha)}$; for a charged particle, we obtain ${\it s}\sim E^{\alpha/2(1-\alpha)}$. Thus, "quantum mirrors" --surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero-- can also exist for charged particles.