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Temperature-Induced Quantum Migration and local heat capacity in confined Fermi gases

Altug Sisman* and Jonas Fransson†

  • *Contact author: altug.sisman@physics.uu.se
  • †Contact author: jonas.fransson@physics.uu.se
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Phys. Rev. E 113, 044129 – Published 22 April, 2026

DOI: https://doi.org/10.1103/3ct1-tbh8

Abstract

Temperature-Induced Quantum Migration (TIQM) is a macroscopic quantum phenomenon that fundamentally reshapes the local thermodynamics of confined systems. While previously explored in Maxwell-Boltzmann and Bose gases, we here extend the TIQM framework to noninteracting Fermi gases confined in anisometric rectangular domains. These domains are characterized by DI, representing the number of dimensions that remain unconfined. We derive the local heat capacity and demonstrate that the standard temperature derivative of local energy yields unphysical negative regions, a discrepancy resolved by the TIQM correction. We show that quantum degeneracy in Fermi gases generally suppresses the TIQM contribution to global heat capacity compared to other statistics, yet it drives a distinct redistribution of local heat capacity. Notably, for the most constrained case (DI=0), a Schottky-type anomaly emerges at low densities, which is progressively “washed out” by increasing dimensionality (DI=1,2). Based on an idealized noninteracting model, our calculations suggest that a measurable (22%) enhancement in the local-to-global electronic heat capacity ratio could emerge at approximately 84 nm from the longitudinal boundaries of a 12×12×5600 nm3 bismuth nanowire at 30 K, offering a potential experimental signature for TIQM. These results complete a systematic trilogy of studies across all fundamental quantum statistics, establishing TIQM as a necessary correction for the local thermodynamics of nanoscale devices.

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Phys. Rev. E 113, 044129– Published 22 April, 2026
  • Received 17 February 2026
  • Accepted 23 March 2026
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