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Finite Size Effects in Equations of State under non-trivial Boundary Conditions

We study free particles in a one-dimensional box with combinations of two types of boundary conditions: the Dirichlet condition and a one-parameter family of quasi-Neumann conditions at the two walls. We calculate energy spectra approximately and obtain equations of state having the same (one-dimensional) volume dependence as van der Waals equations of state. The dependence of the equations of state is examined for particles obeying Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac statistics. Our results suggest that the deviation from ideal gas may also be realized as finite size effects due to the interaction between the particles and the walls.

preprint2009arXivOpen access
Nobuhiro Yonezawa
cond-mat.stat-mechmath-phmath.MPquant-ph
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Nobuhiro Yonezawa

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