DOI: 10.1063/1.533185. Large deviations for ideal quantum systems

Large deviations for ideal quantum systems

10.1063/1.533185

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

We consider a general d-dimensional quantum system of non-interacting particles in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain Λ of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of Λ, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.

Bibliography

Lebowitz, J. L., Lenci, M., & Spohn, H. (2000). Large deviations for ideal quantum systems. Journal of Mathematical Physics, 41(3), 1224â1243.

Authors 3

Joel L. Lebowitz (first)
Marco Lenci (additional)
Herbert Spohn (additional)

References 29 Referenced 22

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10.1007/BF00250473 / Arch. Ration. Mech. Anal. / The free energy of a macroscopic system (1964)
{'key': '2024020613513378300_r3'}
{'key': '2024020613513378300_r4'}
{'key': '2024020613513378300_r5'}
10.1007/BF00319293 / Probab. Theory Related Fields / Large deviations for Gibbs random fields (1988)
{'key': '2024020613513378300_r7'}
10.1007/BF01218477 / Commun. Math. Phys. / The large deviation principle and some models of an interacting boson gas (1988)
{'key': '2024020613513378300_r9', 'first-page': '1063', 'article-title': 'The large deviation principle for the Kac distribution', 'volume': '61', 'year': '1986', 'journal-title': 'Helv. Phys. Acta'} / Helv. Phys. Acta / The large deviation principle for the Kac distribution (1986)
10.1007/BF02096732 / Commun. Math. Phys. / The full diagonal model of a Bose gas (1993)
10.1007/BF02096872 / Commun. Math. Phys. / Dynamics of fluctuations for quantum lattice systems (1990)
10.1063/1.531343 / J. Math. Phys. / Lie algebra of anomalously scaled fluctuations (1995)
10.1088/0305-4470/29/13/010 / J. Phys. A / General one-particle fluctuations of the ideal Bose gas (1996)
10.1007/BF01646633 / Commun. Math. Phys. / Asymptotic free energy of a system with periodic boundary conditions (1970)
10.1007/BF01048183 / J. Stat. Phys. / Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory (1993)
{'key': '2024020613513378300_r16'}
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{'key': '2024020613513378300_r21'}
{'key': '2024020613513378300_r22'}
{'key': '2024020613513378300_r23', 'first-page': '169', 'article-title': 'The ideal Bose-Einstein gas, revisited', 'volume': '32C', 'year': '1977', 'journal-title': 'Phys. Rev.'} / Phys. Rev. / The ideal Bose-Einstein gas, revisited (1977)
{'key': '2024020613513378300_r24', 'first-page': '1271', 'article-title': 'A general theory of Bose-Einstein condensation', 'volume': '59', 'year': '1986', 'journal-title': 'Helv. Phys. Acta'} / Helv. Phys. Acta / A general theory of Bose-Einstein condensation (1986)
10.1007/BF01645656 / Commun. Math. Phys. / Infinite volume of the canonical free Bose gas states on the Weyl algebra (1973)
{'key': '2024020613513378300_r26', 'first-page': '1289', 'article-title': 'On the general theory of Bose-Einstein condensation and the state of the free Boson gas', 'volume': '59', 'year': '1986', 'journal-title': 'Helv. Phys. Acta'} / Helv. Phys. Acta / On the general theory of Bose-Einstein condensation and the state of the free Boson gas (1986)
{'key': '2024020613513378300_r27'}
{'key': '2024020613513378300_r28'}
{'key': '2024020613513378300_r29'}

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:59 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 9:21 a.m.)
Indexed	1 year, 6 months ago (Feb. 6, 2024, 9:40 a.m.)
Issued	25 years, 5 months ago (March 1, 2000)
Published	25 years, 5 months ago (March 1, 2000)
Published Print	25 years, 5 months ago (March 1, 2000)

Funders 0

None

BibTeX

@article{Lebowitz_2000, title={Large deviations for ideal quantum systems}, volume={41}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.533185}, DOI={10.1063/1.533185}, number={3}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Lebowitz, Joel L. and Lenci, Marco and Spohn, Herbert}, year={2000}, month=mar, pages={1224–1243} }

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