Non-adiabaticity and improved back-reaction

TL;DR

This paper investigates quantum back-reaction in time-dependent quantum systems, introducing improved adiabatic methods, analyzing instabilities, and applying results to complex phenomena like D-branes, inflation, and black holes.

Contribution

It develops a canonical transformation approach for better adiabatic expansion, studies instabilities at critical velocities, and extends techniques to quantum field theory and fermions.

Findings

Identified an instability at a critical velocity in the classical system.

Extended the analysis to quantum systems and field theories.

Provided a solvable model for non-adiabatic back-reaction effects.

Abstract

We treat quantum back-reaction in time dependent processes for quantum field theory in various simplified models. The first example is a harmonic oscillator whose frequency depends on a second quantum variable $x$. Beginning with a classical analysis, we show how using a particular canonical transformation the system can be described by an improved adiabatic expansion with a velocity dependent force for $x$. We find an instability at a critical velocity that prevents integrating out the oscillator degree of freedom in the new variables. We extend this calculation to the quantum system and to field theory and describe how to study fermions with similar techniques. Finally, we set up a model with an abrupt change in the oscillator whose quantum mechanics can be solved exactly so that one can study the effects of back-reaction of a fully non-adiabatic change in a controlled setting. We comment on applications of these general results to the physics of D-branes, inflation, and black holes in AdS/CFT.