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

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

2009-04-07

arxiv.org/abs/0904.1134v4

Prog. Theor. Phys. 123 (2009), 35-50

Physics

Mathematical Physics

18pages, 3 figures

Scientific paper

10.1143/PTP.123.35

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.

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