Abstract
In a previous paper the statistics of a system of identical particles moving in an external field depending on a scale factor has been studied in the classical framework. In particular the case in which the scale factor increases to infinity (macroscopic limit) has been considered.
In the present paper the quantum extension is discussed.
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References
Gatés, D. J., Penrose, O.: The van der Waals limit for classical systems. I. A variational Principle. Commun. math. Phys.15, 255 (1969).
Millard, K.: A statistical mechanical approach to the problem of a fluid in an external field. J. Math. Phys.13, 222 (1972).
Garrod, C., Simmons, C.: Rigorous statistical mechanics for non-uniform systems. J. Math. Phys., (August 1972).
Marchioro, C., Presutti, E.: Thermodynamics of particle systems in the presence of external macroscopic fields. I. Classical case. Commun. math. Phys.27, 146 (1972).
Lieb, E.: Quantum-mechanical extension of the Lebowitz-Penrose theorem on the van der Waals theory. J. Math. Phys.7, 1016 (1966).
Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. math. Phys.18, 127 (1970).
Kato, T.: Perturbation theory for linear operator. Berlin: Springer 1966.
Sobolev, S. L.: Application of the functional analysis in mathematical physics, American Mathematical Society, Providence, Rhode Island, 1963.
Robinson, D. W. Statistical mechanics of quantum mechanical particles with hard cores. Commun. math. Phys.16, 290 (1970).
Robinson, D. W.: The thermodynamic pressure in quantum statistical mechanics, lecture notes in Physics. Berlin-Heidelberg-New York: Springer 1971.
Ruelle, D.: Statistical mechanics. Rigorous results. New York: Benjamin 1969.
Novikov, I. D.: Funct. Anal. and Appl.3, 71 (1969).
Gallavotti, G., Lupini: On the boundary conditions in quantum statistical mechanics. (Unpublished preprint.)
Marchioro, C., Presutti, E.: Exact statistical model in one dimension. Lettere Nuovo Cimento 4, 488 (197 ?).
Sutherland, B.: Quantum many-body in one dimension: Thermodynamics. J. Math. Phys.12, 251 (1971).
Calogero, F.: Solution of the one-dimensionalN-body problems with quadratic and/or inversely quadratic pair potentials. J. Math. Phys.12, 419 (1971).
Sutherland, B.: Exact results for a quantum many-body problem in one dimension. II. Phys. Rev.5, 1372 (1972).
Gallavotti, G., Marchioro, C: On the calculation of an integral. J. Math. Anal. Appl. (submitted to) (1972).
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Research supported in part by the Consiglio Nazionale delle Ricerche. (G.N.F.M.A.M.F.I.)
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Marchioro, C., Presutti, E. Thermodynamics of particle systems in the presence of external macroscopic fields. Commun.Math. Phys. 29, 265–284 (1973). https://doi.org/10.1007/BF01646130
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DOI: https://doi.org/10.1007/BF01646130