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Fermionic condensation

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Thermodynamics of the Bose gas follows from the thermodynamics of the Fermi gas. ... I showed that the equivalent Bose system condenses; ... – PowerPoint PPT presentation

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Title: Fermionic condensation


1
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.

2
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.

3
Bosons and fermions
4
Bosons and fermions
Robert M. May, Phys. Rev. 135, A1515 (1964)
5
Intermediate statistics (FES)
F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991)
6
Reason for the universality
7
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.

8
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!
9
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

10
A proper way to account for the fermionic
condensation is by the Exclusion Statistics
Transformation
11
General EST
12
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13
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14
What do we know about bosons and fermions?
15
  • But, if the fermionic condensation happens before
    the first order phase transition

The order of the phase transition increases
16
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.
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