Interpreting Liouvillian Eigenmodes: Quantized Orbits in Dissipative Systems
Abstract
In closed quantum dynamics, energy eigenstates represent physical excitations which, for systems with a classical limit, localize on quantized orbits in phase space. Such a picture is lacking in open systems: Liouvillians have distinct right and left eigenstates that decay with time and are difficult to interpret. We recover a physical correspondence by introducing a gauge-invariant quasiprobability measure combining right and left eigenstates that interprets a Liouvillian mode as a set of coherences, allowing one to visualize the modes as quasiprobability distributions in a ``doubled'' phase space. Using this measure we show that, remarkably, a damped oscillator retains its quantized ``orbits'' for a large class of linear and nonlinear loss, with measurable signatures. A thermal bath broadens these orbits, similar to energy levels, leading to a characteristic multistage relaxation. This provides an experimentally accessible open-system analog of the eigenstate-orbit correspondence underlying semiclassical quantization. For quadratic systems, our results yield dissipative analogs of invariant tori - a central concept in Hamiltonian systems.
Related
- Self-Trapping and Liouvillian Spectral Transitions in a Dissipative Bose-Hubbard Dimer
- A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra
- Action-Quantized Scar Multiplets and Dissipative Cat States from Fractal Period-Locking in the Open Quantum Baker Map
- Liouvillian spectral snapshots: A reduced-subspace approach for time-dependent and noisy open quantum systems
- Coherence-Mediated Boundary Control of the Liouvillian Gap in Nonreciprocal Open Quantum Systems
BibTeX
@misc{thomas2026interpreting,
title = {{Interpreting Liouvillian Eigenmodes: Quantized Orbits in Dissipative Systems}},
author = {Ashlin V Thomas and Felix Fritzsch and Masudul Haque and Shovan Dutta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.20271},
eprint = {2606.20271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20271},
}
RIS
TY - UNPB
TI - Interpreting Liouvillian Eigenmodes: Quantized Orbits in Dissipative Systems
AU - Ashlin V Thomas
AU - Felix Fritzsch
AU - Masudul Haque
AU - Shovan Dutta
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2606.20271
UR - https://arxiv.org/abs/2606.20271
AB - In closed quantum dynamics, energy eigenstates represent physical excitations which, for systems with a classical limit, localize on quantized orbits in phase space. Such a picture is lacking in open systems: Liouvillians have distinct right and left eigenstates that decay with time and are difficult to interpret. We recover a physical correspondence by introducing a gauge-invariant quasiprobability measure combining right and left eigenstates that interprets a Liouvillian mode as a set of coherences, allowing one to visualize the modes as quasiprobability distributions in a ``doubled'' phase space. Using this measure we show that, remarkably, a damped oscillator retains its quantized ``orbits'' for a large class of linear and nonlinear loss, with measurable signatures. A thermal bath broadens these orbits, similar to energy levels, leading to a characteristic multistage relaxation. This provides an experimentally accessible open-system analog of the eigenstate-orbit correspondence underlying semiclassical quantization. For quadratic systems, our results yield dissipative analogs of invariant tori - a central concept in Hamiltonian systems.
ER -