6 research outputs found
The BCS-Bose Crossover Theory
We contrast {\it four} distinct versions of the BCS-Bose statistical
crossover theory according to the form assumed for the electron-number equation
that accompanies the BCS gap equation. The four versions correspond to
explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper
pairs (CPs), or both in equal proportions, or only either kind. This follows
from a recent generalization of the Bose-Einstein condensation (GBEC)
statistical theory that includes not boson-boson interactions but rather 2e-
and also (without loss of generality) 2h-CPs interacting with unpaired
electrons and holes in a single-band model that is easily converted into a
two-band model. The GBEC theory is essentially an extension of the
Friedberg-T.D. Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It
can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and
noncondensed states are separately equal, the BCS gap equation for all
temperatures and couplings as well as the zero-temperature BCS
(rigorous-upper-bound) condensation energy for all couplings. But ignoring
either 2h- {\it or} 2e-CPs it can do neither. In particular, only {\it half}
the BCS condensation energy is obtained in the two crossover versions ignoring
either kind of CPs. We show how critical temperatures from the original
BCS-Bose crossover theory in 2D require unphysically large couplings for the
Cooper/BCS model interaction to differ significantly from the s of
ordinary BCS theory (where the number equation is substituted by the assumption
that the chemical potential equals the Fermi energy).Comment: thirteen pages including two figures. Physica C (in press, 2007
Dynamics of populations, movements and responses to climatic changes in North Africa and the Nile Valley
Fluid-dynamical description of the gap fluctuations of two trapped fermion species
We apply a recent generalisation of the fluid-dynamical scheme
developed for two trapped fermion species with pairing interactions
to examine the fluctuations of the gap density coupled to the
particle transition density at low energy. The dynamical scheme
satisfies Kohn's theorem for both the particle density and the
pairing gap. We analyse the form of the gap fluctuations in a
spherical trap in terms of their multipolarity and the interaction
strength, and find that coupling to the particle density produces
considerable stiffness of the gap transition density together with
compression towards the centre of the trap