The response of a quantum system to a collision: an autonomous derivation of Kubo's formula

TL;DR

This paper derives Kubo's formula for quantum system response to collisions using scattering theory, revealing a fluctuation-dissipation relation and showing how the formula emerges in the Born approximation.

Contribution

It provides an autonomous derivation of Kubo's formula within a scattering framework, connecting collision dynamics to linear response theory.

Findings

Derivation of a non-perturbative response function from scattering theory

Identification of a fluctuation-dissipation relation in the quantum collision context

Kubo's formula emerges naturally in the Born approximation

Abstract

We study the response of a quantum system induced by a collision with a quantum particle, using the time-independent framework of scattering theory. After deriving the dynamical map for the quantum system, we show that it encodes a non-perturbative response function obeying a general fluctuation-dissipation relation. We show that Kubo's formula emerges autonomously in the Born approximation, where the time-dependent perturbation is determined by particle's evolution through the potential region.