PreprintCC BY-NC-ND 4.0HAL
Effective Dissipation and Asymptotic Stability in a Finite-Level Quantum System with Wave-Induced Memory
Abstract
We study quantum systems modeled by Liouville-Von Neumann equations, with a finite number of energy levels. The system is coupled to a wave equation, intended to reproduce environmental effects on the quantum system. The whole dynamic is energy conservative, but damping effects are expected to be embodied into the energy exchanges with the environment. We analyse how these effects can effectively damp quantum coherences. We exhibit key mechanisms and structural properties for such a damping to arise, with a neat distinction between pure and mixed cases.
Related
- Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation
- Uniqueness and stability of entropy waves among vanishing dissipation limits from the Navier--Stokes--Fourier System
- Enhanced dissipation and stability threshold for the Navier--Stokes equations near Poiseuille flow
- Sharp linear stability and the absence of enhanced dissipation for Kolmogorov flow in the 2D Navier--Stokes equations with horizontal dissipation
- Energy dissipation and free boundary stability of the Stefan problem
BibTeX
@misc{goudon2026effective,
title = {{Effective Dissipation and Asymptotic Stability in a Finite-Level Quantum System with Wave-Induced Memory}},
author = {Thierry Goudon},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16327},
eprint = {2609.16327},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05749780v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Effective Dissipation and Asymptotic Stability in a Finite-Level Quantum System with Wave-Induced Memory
AU - Thierry Goudon
PY - 2026
DA - 2026/09/14
PB - HAL
DO - 10.48550/arxiv.2609.16327
UR - https://hal.science/hal-05749780v1
AB - We study quantum systems modeled by Liouville-Von Neumann equations, with a finite number of energy levels. The system is coupled to a wave equation, intended to reproduce environmental effects on the quantum system. The whole dynamic is energy conservative, but damping effects are expected to be embodied into the energy exchanges with the environment. We analyse how these effects can effectively damp quantum coherences. We exhibit key mechanisms and structural properties for such a damping to arise, with a neat distinction between pure and mixed cases.
ER -