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

2025/05/06 by Jacob, Samuel L., Goold, John
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2505.03686

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.

Citations

• Sensitivity of a collisional single-atom spin probe
• A Single Atom Thermometer for Ultracold Gases
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems

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