Spectrum of the steady-state distribution function of disordered Lindbladian fermions at large channel number
Abstract
Free fermions coupled to particle gain and loss relax to a Gaussian steady state, in which every natural orbital has its own occupation. We find the distribution of these occupations ϱst for a random Hamiltonian coupled to many random gain and loss channels. Each orbital is filled and emptied at its own rates, and the Hamiltonian, moving particles across the levels during their lifetime, averages the differences between the orbitals. We show that this averaging is incomplete: the spread of the occupations decreases only as the inverse square root of the number of channels per level. At large system size the distribution depends on the grain Hamiltonian only through its density of states ν(E). The spread is bounded by the baths alone: even Hamiltonians with unbounded, heavy-tailed spectra cannot widen it beyond this bound. The spread suppresses the particle-number fluctuations below their binomial value.
Related
- Measurement-induced phase transitions in disordered fermions
- Airy distribution of the quenched spectral form factor in non-interacting fermions
- The quadratic density response function for non-interacting fermions at arbitrary temperature
- Typed Transverse Momentum Parton distribution function computations
- A seamless workflow for STXM-NEXAFS data analysis using napari: implementation of an ROI spectrum extraction function
BibTeX
@misc{parfenov2026spectrum,
title = {{Spectrum of the steady-state distribution function of disordered Lindbladian fermions at large channel number}},
author = {Maksim Parfenov and Igor Burmistrov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38805},
eprint = {2610.38805},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38805},
}
RIS
TY - UNPB
TI - Spectrum of the steady-state distribution function of disordered Lindbladian fermions at large channel number
AU - Maksim Parfenov
AU - Igor Burmistrov
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38805
UR - https://arxiv.org/abs/2610.38805
AB - Free fermions coupled to particle gain and loss relax to a Gaussian steady state, in which every natural orbital has its own occupation. We find the distribution of these occupations ϱ_st for a random Hamiltonian coupled to many random gain and loss channels. Each orbital is filled and emptied at its own rates, and the Hamiltonian, moving particles across the levels during their lifetime, averages the differences between the orbitals. We show that this averaging is incomplete: the spread of the occupations decreases only as the inverse square root of the number of channels per level. At large system size the distribution depends on the grain Hamiltonian only through its density of states ν(E). The spread is bounded by the baths alone: even Hamiltonians with unbounded, heavy-tailed spectra cannot widen it beyond this bound. The spread suppresses the particle-number fluctuations below their binomial value.
ER -