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

Оригинал: Стишов С М «Квантовые эффекты в системе "больцмановских" твёрдых сфер» УФН 189 659–664 (2019); DOI: 10.3367/UFNr.2018.07.038399

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