Quantum Brownian motion in a temperature gradient
Abstract
When a classical Brownian particle is subjected to a temperature gradient it can undergo thermophoresis, i.e., the particle gets transported towards the colder regions of the environment, which bears relevant consequences to nonequilibrium self-organization. Here, we investigate how the quantum Brownian motion is affected by a temperature gradient. We employ a recently proposed generalized system-plus-reservoir model, where one assumes a continuum field of thermal baths. As our main result, we obtain the quantum influence functional, within the Feynmann-Vernon path integral approach. To test convergence, we derive an effective Langevin equation for the center of mass of the quantum wavepacket, and show that it coincides with the classical Langevin equation at high temperatures. Both the fully quantum (low temperatures) and the semiclassical (high temperature) limits show signatures of quantum thermophoresis in the quantum Brownian motion, a so far unexplored effect.
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BibTeX
@misc{afonso2026quantum,
title = {{Quantum Brownian motion in a temperature gradient}},
author = {Ricardo J. S. Afonso and Pedro V. Paraguassú and Thiago Werlang and Daniel Valente},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17239},
eprint = {2609.17239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17239},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Brownian motion in a temperature gradient
AU - Ricardo J. S. Afonso
AU - Pedro V. Paraguassú
AU - Thiago Werlang
AU - Daniel Valente
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17239
UR - https://arxiv.org/abs/2609.17239
AB - When a classical Brownian particle is subjected to a temperature gradient it can undergo thermophoresis, i.e., the particle gets transported towards the colder regions of the environment, which bears relevant consequences to nonequilibrium self-organization. Here, we investigate how the quantum Brownian motion is affected by a temperature gradient. We employ a recently proposed generalized system-plus-reservoir model, where one assumes a continuum field of thermal baths. As our main result, we obtain the quantum influence functional, within the Feynmann-Vernon path integral approach. To test convergence, we derive an effective Langevin equation for the center of mass of the quantum wavepacket, and show that it coincides with the classical Langevin equation at high temperatures. Both the fully quantum (low temperatures) and the semiclassical (high temperature) limits show signatures of quantum thermophoresis in the quantum Brownian motion, a so far unexplored effect.
ER -