Fermionic condensation

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Fermionic condensation
Dragos-Victor Anghel University of Oslo

• Related publications
• D. V. Anghel, Exclusion Statistics Transformation
  and Ensemble Equivalence Tested From a Different
  Perspective, submitted to J. Math. Phys.,
  cond-mat/0310377.
• D. V. Anghel, Condensation in ideal Fermi gases,
  J. Phys. A Math. Gen. 36, L577-L583 (2003)
  cond-mat/0310248.
• D. V. Anghel, Gases in two dimensions universal
  thermodynamics and its consequences, J. Phys. A
  Math. Gen. 35, 7255-7267 (2002),
  cond-mat/0105089.

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Outline

• Universal thermodynamics in 2D systems
• microscopic reason for the universality
• EST in 2D
• extension of EST to systems of general spectra
• condensation
• thermodynamic equivalence
• effects of condensation.

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Bosons and fermions
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Bosons and fermions
Robert M. May, Phys. Rev. 135, A1515 (1964)
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Intermediate statistics (FES)
F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991)
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Reason for the universality
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Realization of FES

• M.V.N. Murthy and R. Shankar, Phys. Rev. Lett.
  73, 3331 (1994)
• T.H. Hansson, J.M. Leinaas, and S. Viefers, Nucl.
  Phys. B 470, 291 (1996)
• S.B. Isakov and S. Viefers, Int. J. Mod. Phys. A
  12, 1895 (1997)
• T.H. Hansson, J.M. Leinaas, and S. Viefers, Phys.
  Rev. Lett. 86, 2930 (2001)
• M.V.N. Murthy and R. Shankar, Phys. Rev. B 60,
  6517 (1999)
• Z.N.C. Ha, Phys. Rev. Lett. 73, 1574 (1994)
• D.V. Anghel, J. Phys. A Math. Gen. 35, (2002)
• D.V. Anghel, cond-mat/0310377.

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What happens if there is an interval with all the
energy levels occupied?
I calculate the partition function
its derivative
I get first order phase transition!
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Could we have a condensate in the ideal system?

• sgt0 always a condensate
• s0 the gas will condense
• slt0 the gas will condense ? first order phase
  transition

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A proper way to account for the fermionic
condensation is by the Exclusion Statistics
Transformation
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General EST
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What do we know about bosons and fermions?
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• But, if the fermionic condensation happens before
  the first order phase transition

The order of the phase transition increases
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Conclusions

• I presented the basic idea of Exclusion
  Statistics Transformation
• I showed that the equivalent Bose system
  condenses
• the BEC is related to the fermionic condensation
• the idea of EST questions the ensemble
  equivalence in Fermi systems
• I gave examples of the effects of fermionic
  condensation.