Quantum effective action for dissipative semiclassical dynamics
Abstract
Using the quantum effective action in the Schwinger-Keldysh formalism, we derive quantum-thermal corrections to the semiclassical dynamics of a dissipative system described by a macroscopic degree of freedom. We discuss the connection with the Ehrenfest theorem and, within the local potential approximation, obtain the corrections in closed form for arbitrary temperature and damping, showing that as the temperature increases, they cross over from purely quantum to purely thermal. In the low-temperature and weak-damping regime, corrections are set by the zero-point energy of fluctuations evaluated at the classical underdamped frequency, closely paralleling the conservative case, which allows us to go to higher order in the derivative expansion. We apply these general results to the resistively and capacitively shunted superconducting Josephson junction and to an elongated bosonic junction, where corrections can reach the percent level under realistic conditions.
Versions
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BibTeX
@misc{vianello2026quantum,
title = {{Quantum effective action for dissipative semiclassical dynamics}},
author = {Cesare Vianello and Andrea Bardin and Luca Salasnich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.19643},
eprint = {2605.19643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19643},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum effective action for dissipative semiclassical dynamics
AU - Cesare Vianello
AU - Andrea Bardin
AU - Luca Salasnich
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2605.19643
UR - https://arxiv.org/abs/2605.19643
AB - Using the quantum effective action in the Schwinger-Keldysh formalism, we derive quantum-thermal corrections to the semiclassical dynamics of a dissipative system described by a macroscopic degree of freedom. We discuss the connection with the Ehrenfest theorem and, within the local potential approximation, obtain the corrections in closed form for arbitrary temperature and damping, showing that as the temperature increases, they cross over from purely quantum to purely thermal. In the low-temperature and weak-damping regime, corrections are set by the zero-point energy of fluctuations evaluated at the classical underdamped frequency, closely paralleling the conservative case, which allows us to go to higher order in the derivative expansion. We apply these general results to the resistively and capacitively shunted superconducting Josephson junction and to an elongated bosonic junction, where corrections can reach the percent level under realistic conditions.
ER -