Abstract
The surface term in the thermodynamic pressure of free quantum gases is proved to exist and is evaluated. Detailed proofs are given for parallelepipedic domains with Dirichlet, periodic, and Neumann boundary conditions and for more general domains with Dirichlet boundary conditions.
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References
D. Ruelle,Statistical Mechanics, Benjamin, New York, 1969.
D. W. Robinson,The Thermodynamic Pressure in Quantum Statistical Mechanics, Lecture Notes in Physics, Vol. 9, Springer-Verlag, 1971.
J. L. Lebowitz,Ann. Rev. Phys. Chem. 19:389 (1968).
M. E. Fisher and J. L. Lebowitz,Commun. Math. Phys. 19:251 (1970).
H. Frölich,Physica (Utrecht) 4:406 (1937); D. A. Krueger,Phys. Rev. 172:211 (1968); R. E. Dewar and N. E. Frankel,Phys. Rev. 165:283 (1968); M. E. Fisher, G. A. T. Allan, and M. N. Barber, inProc. IUPAP Conf. on Statistical Mechanics, Chicago, 1971; R. K. Pathria,Phys. Lett. 35A:351 (1971).
R. Balian and C. Bloch,Ann. Phys. (N.Y.) 60:401 (1970).
I. Stakgold,Boundary Value Problems of Mathematical Physics, Vol. II, The Macmillan Co., New York, 1968.
K. Huang,Statistical Mechanics, Wiley, New York, 1963.
E. W. Montroll and J. C. Ward,Phys. Fluids 1:55 (1958).
J. Ginibre,Some Applications of Functional Integration in Statistical Mechanics, Lectures delivered at les Houches, 1970.
N. Angelescu and G. Nenciu,On the Independence of the Thermodynamic Pressure of the Boundary Conditions in Quantum Statistical Mechanics (to be published).
G. Nenciu (to be published).
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Nenciu, G. On the surface contribution to the grand-canonical pressure of free quantum gases. J Stat Phys 7, 119–130 (1973). https://doi.org/10.1007/BF01024210
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DOI: https://doi.org/10.1007/BF01024210