Super-Adiabatic Particle Number in Schwinger and de Sitter Particle Production

TL;DR

This paper introduces a super-adiabatic basis for analyzing particle production in electric fields and de Sitter space, revealing smooth evolution and quantum interference effects, with implications for understanding particle creation in curved spacetime.

Contribution

It defines a super-adiabatic particle number that improves the analysis of particle production, incorporating quantum interference effects and smoothing the evolution in time-dependent backgrounds.

Findings

Super-adiabatic basis smooths particle number evolution.

Quantum interference effects depend on spacetime dimensionality.

Constructive and destructive interference observed in de Sitter space.

Abstract

We consider the time evolution of the adiabatic particle number in both time-dependent electric fields and in de Sitter spaces, and define a super-adiabatic particle number in which the (divergent) adiabatic expansion is truncated at optimal order. In this super-adiabatic basis, the particle number evolves smoothly in time, according to Berry's universal adiabatic smoothing of the Stokes phenomenon. This super-adiabatic basis also illustrates clearly the quantum interference effects associated with particle production, in particular for sequences of time-dependent electric field pulses, and in eternal de Sitter space where there is constructive interference in even dimensions, and destructive interference in odd dimensions.