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Perturbation theory in a microcanonical ensemble

Author

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  • Pradhan, Ritapriya
  • Bhattacharjee, Jayanta K.

Abstract

The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, mainly the canonical and grand canonical ensembles have been used. In this article we show how the microcanonical ensemble can be directly used to carry out perturbation theory for both non-interacting and interacting systems. We obtain the first non-trivial order answers for the specific heat of anharmonic oscillators and for the virial expansion in real gases. They are in exact agreement with the results obtained from the canonical ensemble. In addition, we show how crossover functions for the specific heat of anharmonic oscillators can be constructed using a microcanonical ensemble and also how the subsequent terms of the virial expansion can be obtained. We find that if we consider quantum free particles in a one-dimensional box of extension L, then both the ensembles give an unusual result for the first correction to the specific heat in the high temperature limit.

Suggested Citation

  • Pradhan, Ritapriya & Bhattacharjee, Jayanta K., 2024. "Perturbation theory in a microcanonical ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    • Handle: RePEc:eee:phsmap:v:634:y:2024:i:c:s0378437123009792
    DOI: 10.1016/j.physa.2023.129424
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    References listed on IDEAS

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    1. Nicole Yunger Halpern & Philippe Faist & Jonathan Oppenheim & Andreas Winter, 2016. "Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges," Nature Communications, Nature, vol. 7(1), pages 1-7, November.
    2. Lynden-Bell, D., 1999. "Negative specific heat in astronomy, physics and chemistry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 293-304.
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