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Boundary effect of a partition in a quantum well
Tamas Fulop, Izumi Tsutsui
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0612011
- categories:
- quant-ph
- comments:
- LaTeX (with iopart.cls, iopart10.clo and iopart12.clo), 28 pages, 17
figures
- doi:
- 10.1088/1751-8113/40/17/013
- arxiv_id:
- quant-ph/0612011
- journal_ref:
- J. Phys. A: Math. Theor. 40 (2007) 4585-4608
- created:
- 2006-12-01
- updated:
- 2007-05-09
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