Spectral and steady-state properties of fermionic random quadratic Liouvillians
Abstract
We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by M random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, m=M/(2NF), we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for m=1/2 and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below m=1/2, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.
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BibTeX
@article{costa2026spectral,
title = {{Spectral and steady-state properties of fermionic random quadratic Liouvillians}},
author = {João Costa and Pedro Ribeiro and Andrea de Luca and Tomaž Prosen and Lucas Sá},
journal = {SciPost Physics},
year = {2026},
month = oct,
doi = {10.21468/scipostphys.15.4.145},
eprint = {2210.07959},
archivePrefix = {arXiv},
url = {https://hal.science/hal-03836847v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Spectral and steady-state properties of fermionic random quadratic Liouvillians
AU - João Costa
AU - Pedro Ribeiro
AU - Andrea de Luca
AU - Tomaž Prosen
AU - Lucas Sá
PY - 2026
DA - 2026/10/28
JO - SciPost Physics
DO - 10.21468/scipostphys.15.4.145
UR - https://hal.science/hal-03836847v1
AB - We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by M random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, m=M/(2N_F), we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for m=1/2 and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below m=1/2, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.
SN - 2542-4653
ER -