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Application of non-commutative algebra to a soluble fermionic model

Author

Listed:
  • Charret, I.C.
  • Silva, E.V.Corrêa
  • de Souza, S.M.
  • Santos, O.Rojas
  • Thomaz, M.T.
  • Carneiro, C.E.I.

Abstract

We explore the properties of the non-commutative Grassmann algebra to obtain the high-temperature expansion of the grand canonical partition function for self-interacting fermionic systems. As an application, we consider the anharmonic fermionic oscillator, the simplest model in Quantum Mechanics with self-interacting fermions that is exactly soluble. The knowledge of the exact expression for its grand canonical partition function enables us to check the β-expansion obtained using our Grassmann-algebra-based technique.

Suggested Citation

  • Charret, I.C. & Silva, E.V.Corrêa & de Souza, S.M. & Santos, O.Rojas & Thomaz, M.T. & Carneiro, C.E.I., 1999. "Application of non-commutative algebra to a soluble fermionic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(1), pages 204-221.
  • Handle: RePEc:eee:phsmap:v:264:y:1999:i:1:p:204-221 DOI: 10.1016/S0378-4371(98)00398-7
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    References listed on IDEAS

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    1. Eliazar, Iddo & Klafter, Joseph, 2006. "Growth-collapse and decay-surge evolutions, and geometric Langevin equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 106-128.
    2. Hasumi, Tomohiro & Akimoto, Takuma & Aizawa, Yoji, 2009. "The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 483-490.
    3. Hasumi, Tomohiro & Akimoto, Takuma & Aizawa, Yoji, 2009. "The Weibull–log Weibull distribution for interoccurrence times of earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 491-498.
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