JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Quantum Mechanics (General and Nonrelativistic)

J. Math. Phys. 53, 012101 (2012); http://dx.doi.org/10.1063/1.3670747 (19 pages)

The gap equation for spin-polarized fermions

Abraham Freiji1, Christian Hainzl2, and Robert Seiringer3

1Department of Neurology, UAB, SC 350, 1530 3rd Ave S, Birmingham, Alabama 35294, USA
2Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
3Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

View MapView Map

(Received 5 July 2011; accepted 23 November 2011; published online 4 January 2012)

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δμ/T) ⩽ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal. 17, 559–567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys. 281, 349–367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B 77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δμ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
    1. Balanced fermionic systems
  2. MAIN RESULTS
    1. Critical temperatures
      1. A more detailed phase diagram
      2. A toy model in one dimension
  3. PRELIMINARIES AND PROOF OF THEOREM 1
  4. BOUNDS ON THE CRITICAL TEMPERATURE
    1. Evaluation of Tδμi
    2. Evaluation of Tδμo
    3. Evaluation of Tδμg and a more detailed phase diagram

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

BCS theory, chemical potential, fermion systems, phase diagrams, polarisation in elementary particle interactions

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3670747

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    Bach, V., Fröhlich, J., and Jonsson, L., “Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions,” J. Math. Phys. 50, 102102 (2009)JMAPAQ000050000010102102000001.

    Hainzl, C. and Seiringer, R., “Critical temperature and energy gap for the BCS equation,” Phys. Rev. B 77, 184517-1–10 435 (2008).


Figures (1)

Access to article objects (figures, tables, multimedia) requires a subscription; log in to view available files.
(Access to supplementary files, where available, is free for this journal.)



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. The gap equation for spin-polarized fermions
  2. Twisted hierarchies associated with the generalized sine-Gordon equation
  3. Bell-polynomial approach and N-soliton solution for the extended Lotka–Volterra equation in plasmas
  4. Dispersion equation and eigenvalues for quantum wells using spectral parameter power series
  5. Periodic orbits and nonintegrability of generalized classical Yang–Mills Hamiltonian systems
Go to AIP Home
Copyright © American Institute of Physics
close