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Quantum Thermodynamics

Correlation functions of harmonic lattices in d-dimensional space

arXiv
Authors: Masafumi Shimojo, Satoshi Ishihara, Hironobu Kataoka, Atsuko Matsukawa, Kazuo Koyama

Year

2025

Paper ID

36424

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

We study the correlation functions between the dynamical variables and between their conjugate momenta at sites of a harmonic lattice in the d-dimensional Euclidean space. We show that at the thermodynamic limit, they can be expressed in terms of Lauricella's C-type hypergeometric series. Furthermore, using these expressions, we explicitly demonstrate that the correlators near the center of the lattice satisfying Diriclet boundary conditions coincide with those for the lattice with the periodic boundary conditions. By utilizing these expressions, we expect to make it easier to create programs that compute fast and highly precise for the quantum information quantities of subsystems within lattices.

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  • This paper contributes to the Quantum Thermodynamics research area in the Quantum Articles archive.
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  • We study the correlation functions between the dynamical variables and between their conjugate momenta at sites of a harmonic lattice in the d-dimensional Euclidean space.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.18958 [2] arXiv https://arxiv.org/abs/2512.18958 [3] Publisher https://arxiv.org/abs/2512.18958

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