• Corpus ID: 255546264

Derivation of the Gross-Pitaevskii Theory for Interacting Fermions in a Trap

@inproceedings{Calignano2022DerivationOT,
  title={Derivation of the Gross-Pitaevskii Theory for Interacting Fermions in a Trap},
  author={Andrea Calignano and Michele Correggi},
  year={2022}
}
We study a dilute gas of interacting fermions at temperature T = 0 and chemical potential µ ∈ R . The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Gross-Pitaevskii theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter 
View PDF on arXiv

References

SHOWING 1-10 OF 24 REFERENCES

Condensation of fermion pairs in a domain

We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles are confined to a domain with Dirichlet…

The External Field Dependence of the BCS Critical Temperature

We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a…

Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs

We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well…

Microscopic Derivation of Ginzburg-Landau Theory

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises…

Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic…

Surface effects in superconductors with corners

  • M. Correggi
  • Physics
    Bollettino dell'Unione Matematica Italiana
  • 2020
We review some recent results on the phenomenon of surface superconductivity in the framework of Ginzburg–Landau theory for extreme type-II materials. In particular, we focus on the response of the…

The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties

We review recent results concerning the mathematical properties of the Bardeen–Cooper–Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in…

Theory of Superconductivity

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is…

Ground State Energy of the Low Density Bose Gas

Now that the properties of low temperature Bose gases at low density, ρ, can be examined exprimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades…

The BCS critical temperature in a weak homogeneous magnetic field

We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order…