dorsal/arxiv
View SchemaBoundary effect of a partition in a quantum well
| Authors | Tamas Fulop, Izumi Tsutsui |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612011 |
| URL | https://arxiv.org/abs/quant-ph/0612011 |
| DOI | 10.1088/1751-8113/40/17/013 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 4585-4608 |
Abstract
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.
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"abstract": "The paper wishes to demonstrate that, in quantum systems with boundaries,\ndifferent boundary conditions can lead to remarkably different physical\nbehaviour. Our seemingly innocent setting is a one dimensional potential well\nthat is divided into two halves by a thin separating wall. The two half wells\nare populated by the same type and number of particles and are kept at the same\ntemperature. The only difference is in the boundary condition imposed at the\ntwo sides of the separating wall, which is the Dirichlet condition from the\nleft and the Neumann condition from the right. The resulting different energy\nspectra cause a difference in the quantum statistically emerging pressure on\nthe two sides. The net force acting on the separating wall proves to be nonzero\nat any temperature and, after a weak decrease in the low temperature domain, to\nincrease and diverge with a square-root-of-temperature asymptotics for high\ntemperatures. These observations hold for both bosonic and fermionic type\nparticles, but with quantitative differences. We work out several analytic\napproximations to explain these differences and the various aspects of the\nfound unexpectedly complex picture.",
"arxiv_id": "quant-ph/0612011",
"authors": [
"Tamas Fulop",
"Izumi Tsutsui"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/17/013",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 4585-4608",
"title": "Boundary effect of a partition in a quantum well",
"url": "https://arxiv.org/abs/quant-ph/0612011"
},
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