Year: 2025
Type: article
Abstract: We investigate thermal effects on density fluctuations in confined classical liquids using phonon quantization. The system is modeled via a massless scalar field between perfectly reflecting parallel planes with Dirichlet, Neumann, and mixed boundary conditions. Exact closed-form expressions are derived for the mean-square mass density, total energy density, and thermodynamic quantities including Helmholtz free energy and entropy densities. Our analysis identifies distinct regimes, namely, a low-temperature quantum regime exhibiting characteristic power-law behavior for each boundary condition, and a high-temperature classical regime where ℏ-independent behavior emerges as expected. A particularly interesting finding shows that while most quantities transition naturally to classical behavior, the mean-square density fluctuation requires explicit consideration of the ℏ→0 limit. The entropy density vanishes at zero temperature, in agreement with the Nernst heat theorem. Numerical analysis confirms our analytical results, particularly the asymptotic temperature behaviors and the intermediate crossover region, in which quantum and classical effects compete. This regime is governed by the energy scale k_{B}T∼ℏu/a, where a is the distance between the planes and u is the sound velocity.
Source: Physical review. E
DOI: 10.1103/f7ps-v71q
Authors: Herondy Mota, K. E. L. de Farias
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1871248702
OpenAlex ID: W4415559850