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Ginzburg-Landau Theory

  • Shigeji Fujita
  • Kei Ito
  • Salvador Godoy
Chapter
The pairon field operator \(\psi^{\dagger}({\bf r},t)\) evolves, following Heisenberg’s equation of motion. If the Hamiltonian \(H\) contains a pairon kinetic energy \(h_{0}\), a condensation energy \(\alpha(<0)\) and a repulsive point-like interpairon interaction \(\beta\delta({\bf r}_{1}-{\bf r}_{2})\), \(\beta(> 0)\), the evolution equation for \(\psi\) is non-linear, from which we derive the Ginzburg-Landau (GL) equation:
$$h_{0}({\bf r},-i\hbar\nabla)\Psi^\prime_{\sigma}({\bf r})+\alpha\Psi^\prime_{\sigma}({\bf r}) +\beta|\Psi^\prime_{\sigma}({\bf r})|^{2}\Psi^\prime_{\sigma}({\bf r})=0$$

Keywords

Density Condition Density Operator Expansion Parameter Free Energy Density Momentum State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of PhysicsState University of New YorkBuffaloUSA
  2. 2.National Center for UniversityTokyoJapan
  3. 3.Department of FísicaUniversidad Nacional Autónoma de MéxicoMéxicoMéxico

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