# ←→

Methodological notes

# Quantum effects in a system of Boltzmann hard spheres

Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russian Federation

Quantum contribution to the energy of the Boltzmann' gas consisting of hard spheres proves to be virtually constant up to very high temperatures where the thermal de Broglie wavelength only makes a small fraction of the solid sphere diameter. Consequently, the heat capacity of the system virtually does not differ from a classical value of (3/2)kB everywhere except the lowest temperature region, where heat capacity as a function of temperature has the 'Debye' form but with a very low Debye temperature of the order of several degrees. The line of equilibrium between quantum crystal and liquid for the 'Boltzmann' system of hard spheres coincides with the classical one with the exception of a very-low-temperature region. High-temperature quantum effects are revealed in the system under consideration in a kind of bare' form, while in the case of more realistic systems or models they can be masked by a complex behavior of other components of the total energy.

 Fulltext is available at IOP
Keywords: quantum hard sphere system, thermal wave length, Boltzmann gas
PACS: 64.70.D−, 67.10.Fj (all)
DOI: 10.3367/UFNe.2018.07.038399
URL: https://ufn.ru/en/articles/2019/6/e/
Citation: Stishov S M "Quantum effects in a system of Boltzmann hard spheres" Phys. Usp. 62 617–622 (2019)
 BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 24th, April 2018, revised: 30th, July 2018, 30th, July 2018

Îðèãèíàë: Ñòèøîâ Ñ Ì «Êâàíòîâûå ýôôåêòû â ñèñòåìå "áîëüöìàíîâñêèõ" òâ¸ðäûõ ñôåð» ÓÔÍ 189 659–664 (2019); DOI: 10.3367/UFNr.2018.07.038399

References (29) Similar articles (13) ↓

1. V.V. Brazhkin “Can glassforming liquids be 'simple'?62 623–629 (2019)
2. B.A. Klumov “On melting criteria for complex plasma53 1053–1065 (2010)
3. S.M. Stishov “Notes on phase transitions and the role of spin fluctuations59 866–868 (2016)
4. V.P. Bykov, A.V. Gerasimov, V.O. Turin “Coulomb disintegration of weak electron fluxes and the photocounts38 911–921 (1995)
5. A.M. Ignatov, A.I. Korotchenko et alOn the interpretation of computer simulation of classical Coulomb plasma38 109–114 (1995)
6. P.B. Ivanov “On relativistic motion of a pair of particles having opposite signs of masses55 1232–1238 (2012)
7. M.V. Kuzelev, A.A. Rukhadze “Nonrelativistic quantum theory of stimulated Cherenkov radiation and Compton scattering in a plasma54 375–380 (2011)
8. A.V. Eletskii, A.N. Starostin, M.D. Taran “Quantum corrections to the equilibrium rate constants of inelastic processes48 281–294 (2005)
9. A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects47 797–820 (2004)
10. V.F. Khirnyi, A.A. Kozlovskii “Nonlinear effects and domain instability in oxide ceramics46 657–663 (2003)
11. S.L. Sobolev “Local non-equilibrium transport models40 1043–1053 (1997)
12. V.N. Tsytovich “Collective effects of plasma particles in bremsstrahlung38 87–108 (1995)
13. A.A. Andronov, Yu.A. Ryzhov “An infinity of the classical theory of fluctuations in a nondegenerate electron gas21 873–878 (1978)

The list is formed automatically.

 © 1918–2020 Uspekhi Fizicheskikh Nauk Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions