Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component
Abstract
Generators of continuous-time quantum Markovian evolution, known as Lindblad operators, play a key role in the theory of open quantum systems. The question of how to define and characterize random Lindblad operators has attracted considerable attention in recent years. Purely dissipative random Lindbladians have been extensively studied using toolboxes of free probability and non-Hermitian random matrix theories, which helped to uncover a characteristic lemon-like spectral support. In this work, we focus on random Lindbladians with a Hamiltonian component. We analyze three ensembles of increasing complexity, designed to illustrate the joint effects of dissipative and Hamiltonian dynamics. While the first two allow for an exact analytic treatment with standard probabilistic and scalar-valued free-probability methods, the most general case requires the more general framework of operator-valued free probability. We explain how the spectral support changes with the relative Hamiltonian strength and the rank of the dissipative component and characterize the effect of Hamiltonian-induced spectral squeezing.
Related
- Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
- Spectra: Exact Component Transport for Test-Time Prior Adaptation in Simulation-Based Inference
- Hamiltonian-Type Spectral Functionals for Time-Dependent Perturbed Hodge--de Rham Operators
- Hamiltonian Monte Carlo vs. event-chain Monte Carlo: An appraisal of sampling strategies beyond the diffusive regime
- Uniform approximation of spectra of linear second order differential operators via discrete sine transform based discretisation
BibTeX
@misc{hontarenko2026beyond,
title = {{Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component}},
author = {Mykhailo Hontarenko and Wojciech Tarnowski and Sergey Denisov and Karol Życzkowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19261},
eprint = {2610.19261},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19261},
}
RIS
TY - UNPB
TI - Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component
AU - Mykhailo Hontarenko
AU - Wojciech Tarnowski
AU - Sergey Denisov
AU - Karol Życzkowski
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.19261
UR - https://arxiv.org/abs/2610.19261
AB - Generators of continuous-time quantum Markovian evolution, known as Lindblad operators, play a key role in the theory of open quantum systems. The question of how to define and characterize random Lindblad operators has attracted considerable attention in recent years. Purely dissipative random Lindbladians have been extensively studied using toolboxes of free probability and non-Hermitian random matrix theories, which helped to uncover a characteristic lemon-like spectral support. In this work, we focus on random Lindbladians with a Hamiltonian component. We analyze three ensembles of increasing complexity, designed to illustrate the joint effects of dissipative and Hamiltonian dynamics. While the first two allow for an exact analytic treatment with standard probabilistic and scalar-valued free-probability methods, the most general case requires the more general framework of operator-valued free probability. We explain how the spectral support changes with the relative Hamiltonian strength and the rank of the dissipative component and characterize the effect of Hamiltonian-induced spectral squeezing.
ER -