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arXiv · 2505.03686

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

Samuel L. Jacob·John Goold
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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.

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Samuel L. Jacob, John Goold. 2025-05-06. The response of a quantum system to a collision: an autonomous derivation of Kubo's formula. https://doi.org/10.1088/1751-8121%2Fae04b9

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