dorsal/arxiv
View SchemaFermi and Bose pressures in statistical mechanics
| Authors | Loyal Durand |
|---|---|
| Categories | |
| ArXiv ID | physics/0307118 |
| URL | https://arxiv.org/abs/physics/0307118 |
| DOI | 10.1119/1.1737395 |
Abstract
I show how the Fermi and Bose pressures in quantum systems, identified in standard discussions through the use of thermodynamic analogies, can be derived directly in terms of the flow of momentum across a surface by using the quantum mechanical stress tensor. In this approach, analogous to classical kinetic theory, pressure is naturally defined locally, a point which is obvious in terms of the stress-tensor but is hidden in the usual thermodynamic approach. The two approaches are connected by an interesting application of boundary perturbation theory for quantum systems. The treatment leads to a simple interpretation of the pressure in Fermi and Bose systems in terms of the momentum flow encoded in the wave functions. I apply the methods to several problems, investigating the properties of quasi continuous systems, relations for Fermi and Bose pressures, shape-dependent effects and anisotropies, and the treatment of particles in external fields, and note several interesting problems for graduate courses in statistical mechanics that arise naturally in the context of these examples.
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"abstract": "I show how the Fermi and Bose pressures in quantum systems, identified in\nstandard discussions through the use of thermodynamic analogies, can be derived\ndirectly in terms of the flow of momentum across a surface by using the quantum\nmechanical stress tensor. In this approach, analogous to classical kinetic\ntheory, pressure is naturally defined locally, a point which is obvious in\nterms of the stress-tensor but is hidden in the usual thermodynamic approach.\nThe two approaches are connected by an interesting application of boundary\nperturbation theory for quantum systems. The treatment leads to a simple\ninterpretation of the pressure in Fermi and Bose systems in terms of the\nmomentum flow encoded in the wave functions. I apply the methods to several\nproblems, investigating the properties of quasi continuous systems, relations\nfor Fermi and Bose pressures, shape-dependent effects and anisotropies, and the\ntreatment of particles in external fields, and note several interesting\nproblems for graduate courses in statistical mechanics that arise naturally in\nthe context of these examples.",
"arxiv_id": "physics/0307118",
"authors": [
"Loyal Durand"
],
"categories": [
"physics.ed-ph",
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"doi": "10.1119/1.1737395",
"title": "Fermi and Bose pressures in statistical mechanics",
"url": "https://arxiv.org/abs/physics/0307118"
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