Hydrodynamic description of correlation matrix eigenvalues in a finite temperature expanding free fermionic gas
Abstract
A recent work considered the Page curve for entanglement entropy of a freely expanding one-dimensional Fermi gas starting from a finite box (the system) in a zero-temperature initial state that then expands in to a semi-infinite vacuum (the environment). For the case with a single defect at the system-environment junction, it was shown that the Yang-Yang entropy of the system computed from semiclassical hydrodynamics agrees with the microscopically computed entanglement entropy, yielding the Page curve. On the other hand, the environment Yang-Yang entropy showed a monotonic increase. Here, we propose a hydrodynamic description to obtain the eigenvalues of the microscopic correlation matrix for a nonzero temperature freely-expanding Fermi gas. For the system, the phase space density directly gives the correlation matrix eigenvalues and thus, via the Yang-Yang formula, yields the von-Neumann entropy. For the reservoir, a modification of the phase space density is required in the Yang-Yang formula, to incorporate coherences, in order to reproduce accurately the entropy. The hydrodynamic description of correlation matrix eigenvalues also leads to a Levitov-Lesovik type formula for the full-counting-statistics for a finite system in the transient regime. We provide a heuristic derivation of the correlation matrix eigenvalues based on a semiclassical wave-packet picture.
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BibTeX
@misc{naik2026hydrodynamic,
title = {{Hydrodynamic description of correlation matrix eigenvalues in a finite temperature expanding free fermionic gas}},
author = {Atharva Naik and Madhumita Saha and David A. Huse and Manas Kulkarni and Abhishek Dhar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30062},
eprint = {2610.30062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30062},
}
RIS
TY - UNPB
TI - Hydrodynamic description of correlation matrix eigenvalues in a finite temperature expanding free fermionic gas
AU - Atharva Naik
AU - Madhumita Saha
AU - David A. Huse
AU - Manas Kulkarni
AU - Abhishek Dhar
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30062
UR - https://arxiv.org/abs/2610.30062
AB - A recent work considered the Page curve for entanglement entropy of a freely expanding one-dimensional Fermi gas starting from a finite box (the system) in a zero-temperature initial state that then expands in to a semi-infinite vacuum (the environment). For the case with a single defect at the system-environment junction, it was shown that the Yang-Yang entropy of the system computed from semiclassical hydrodynamics agrees with the microscopically computed entanglement entropy, yielding the Page curve. On the other hand, the environment Yang-Yang entropy showed a monotonic increase. Here, we propose a hydrodynamic description to obtain the eigenvalues of the microscopic correlation matrix for a nonzero temperature freely-expanding Fermi gas. For the system, the phase space density directly gives the correlation matrix eigenvalues and thus, via the Yang-Yang formula, yields the von-Neumann entropy. For the reservoir, a modification of the phase space density is required in the Yang-Yang formula, to incorporate coherences, in order to reproduce accurately the entropy. The hydrodynamic description of correlation matrix eigenvalues also leads to a Levitov-Lesovik type formula for the full-counting-statistics for a finite system in the transient regime. We provide a heuristic derivation of the correlation matrix eigenvalues based on a semiclassical wave-packet picture.
ER -