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Fractional approach, quantum statistics, and non-crystalline solids at very low temperatures

Author

Listed:
  • E. K. Lenzi
  • B. F. de Oliveira
  • N. G.C. Astrath
  • L. C. Malacarne
  • R. S. Mendes
  • M. L. Baesso
  • L. R. Evangelista

Abstract

We consider nonlocal effects, obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, to analyze physical properties of non-crystalline solids at very low temperature. By using thermal Green functions, we deduce some experimentally observable quantities such as the particle momentum distribution function, the particle energy distribution function, and the specific heat. The agreement between the results obtained for the specific heat and the experimental data suggests that the approach presented here may be useful as a phenomenological model to investigate thermal properties of non-crystalline solids at low temperature. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • E. K. Lenzi & B. F. de Oliveira & N. G.C. Astrath & L. C. Malacarne & R. S. Mendes & M. L. Baesso & L. R. Evangelista, 2008. "Fractional approach, quantum statistics, and non-crystalline solids at very low temperatures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(2), pages 155-158, March.
    • Handle: RePEc:spr:eurphb:v:62:y:2008:i:2:p:155-158
    DOI: 10.1140/epjb/e2008-00144-7
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    Citations

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    Cited by:

    1. Ishiwata, Ryosuke & Sugiyama, Yūki, 2012. "Relationships between power-law long-range interactions and fractional mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5827-5838.
    2. Ervin Kaminski Lenzi & Luiz Roberto Evangelista & Luciano Rodrigues da Silva, 2023. "Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    3. Giovanni Modanese, 2018. "Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current," Mathematics, MDPI, vol. 6(9), pages 1-14, September.

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