Domain-wall melting in all-to-all QSSEP from random-matrix theory
Abstract
We study the melting of a domain wall in the quantum simple exclusion process with all-to-all hoppings (a.k.a. the charged SYK 2 model). We show that the real-time dynamics of physical quantities of interest can be obtained exploiting spectral results in random matrix theory. We first show that the eigenvalues of the correlation matrix corresponding to the initially charged subsystem evolve according to a Jacobi process, which is defined in terms of a closed system of stochastic differential equations. In turn, this observation allows us to obtain the real-time dynamics of all the eigenvalue moments. We present two physical applications. First, we study the dynamics of the averaged von Neumann entanglement entropy, arriving at a fully explicit expression in the thermodynamic limit. Second, we compute analytically the full-counting statistics of the charge. Our formula allows us to perform a thorough comparison with the full-counting statistics of the classical simple exclusion process. Notably, we show that, in the thermodynamic limit, the quantum and classical full-counting statistics coincide, with no finite-time corrections.
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BibTeX
@article{bernard2026domainwall,
title = {{Domain-wall melting in all-to-all QSSEP from random-matrix theory}},
author = {Denis Bernard and Lorenzo Piroli and Stefano Scopa},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
year = {2026},
month = jul,
doi = {10.1088/1742-5468/ae824a},
eprint = {2604.28151},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05758921v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Domain-wall melting in all-to-all QSSEP from random-matrix theory
AU - Denis Bernard
AU - Lorenzo Piroli
AU - Stefano Scopa
PY - 2026
DA - 2026/07/09
JO - Journal of Statistical Mechanics: Theory and Experiment
DO - 10.1088/1742-5468/ae824a
UR - https://hal.science/hal-05758921v1
AB - We study the melting of a domain wall in the quantum simple exclusion process with all-to-all hoppings (a.k.a. the charged SYK 2 model). We show that the real-time dynamics of physical quantities of interest can be obtained exploiting spectral results in random matrix theory. We first show that the eigenvalues of the correlation matrix corresponding to the initially charged subsystem evolve according to a Jacobi process, which is defined in terms of a closed system of stochastic differential equations. In turn, this observation allows us to obtain the real-time dynamics of all the eigenvalue moments. We present two physical applications. First, we study the dynamics of the averaged von Neumann entanglement entropy, arriving at a fully explicit expression in the thermodynamic limit. Second, we compute analytically the full-counting statistics of the charge. Our formula allows us to perform a thorough comparison with the full-counting statistics of the classical simple exclusion process. Notably, we show that, in the thermodynamic limit, the quantum and classical full-counting statistics coincide, with no finite-time corrections.
SN - 1742-5468
ER -