Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature
Leschke H, Sobolev AV, Spitzer W (2022)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2022
Publisher: Springer Science and Business Media Deutschland GmbH
Series: Operator Theory: Advances and Applications
Book Volume: 289
Pages Range: 477-508
DOI: 10.1007/978-3-031-13851-5_21
Abstract
We study the local and (bipartite) entanglement Rényi entropies of the free Fermi gas in multi-dimensional Euclidean space in thermal equilibrium. We prove positivity of the entanglement entropies with Rényi index γ ≤ 1 for all temperatures T > 0. Furthermore, for general γ > 0 we establish the asymptotics of the entropies for large T and large scaling parameter α > 0 for two different regimes—for fixed chemical potential and also for fixed particle density ρ > 0. In particular, we thereby provide the last remaining building block for a complete proof of our low- and high-temperature results presented (for γ = 1) in J. Phys. A: Math. Theor. 49, 30LT04 (2016); [Corrigendum. 50, 129501 (2017)], but being supported there only by the basic proof ideas.
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APA:
Leschke, H., Sobolev, A.V., & Spitzer, W. (2022). Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature. In (pp. 477-508). Springer Science and Business Media Deutschland GmbH.
MLA:
Leschke, Hajo, Alexander V. Sobolev, and Wolfgang Spitzer. "Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature." Springer Science and Business Media Deutschland GmbH, 2022. 477-508.
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