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Statistical description of an ideal gas in maximum length quantum mechanics

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  • Bensalem, Salaheddine
  • Bouaziz, Djamil

Abstract

We discuss the effects of the recent proposed Generalized Uncertainty Principle (GUP) (Perivolaropoulos, 2017), which includes a maximum length on the thermostatistics of an ideal gas. In the framework of this modified version of quantum mechanics, the deformed Schrödinger equation is solved analytically for a particle in an infinite square-well potential, then the corresponding energy spectrum is extracted. By computing the modified canonical partition function, the thermodynamic properties of the system are investigated within the canonical and microcanonical ensembles; the results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of the minimal length GUP indicates that the maximum length induces fundamentally different effects, which become important at high temperatures and for large space confining the system. Especially, a modified equation of state, similar to that of real gases, emerges in the scope of this new formalism.

Suggested Citation

  • Bensalem, Salaheddine & Bouaziz, Djamil, 2019. "Statistical description of an ideal gas in maximum length quantum mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 583-592.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:583-592
    DOI: 10.1016/j.physa.2019.02.033
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    References listed on IDEAS

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    1. Farhang Matin, L. & Miraboutalebi, S., 2015. "Statistical aspects of harmonic oscillator under minimal length supposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 10-17.
    2. Mirtorabi, M. & Miraboutalebi, S. & Masoudi, A.A. & Farhang Matin, L., 2018. "Quantum gravity modifications of the relativistic ideal gas thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 602-612.
    3. Nozari, Kourosh & Mehdipour, S. Hamid, 2007. "Implications of minimal length scale on the statistical mechanics of ideal gas," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1637-1644.
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    Cited by:

    1. Bensalem, Salaheddine & Bouaziz, Djamil, 2022. "Thermostatistics in deformed space with maximal length," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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