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

• URL: http://arxiv.org/abs/2505.03686v1
• Date: Tue, 06 May 2025 16:32:42 GMT
• Title: The response of a quantum system to a collision: an autonomous derivation of Kubo's formula
• Authors: Samuel L. Jacob, John Goold,
• Abstract summary: We show that the unitary contribution to the dynamics defines a non-perturbative response function obeying a general fluctuation-dissipation relation.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 the unitary contribution to the dynamics defines 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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