7 research outputs found
Cooper pairs as resonances
Using the Bethe-Salpeter (BS) equation, Cooper pairing can be generalized to
include contributions from holes as well as particles from the ground state of
either an ideal Fermi gas (IFG) or of a BCS many-fermion state. The BCS model
interfermion interaction is employed throughout. In contrast to the
better-known original Cooper pair problem for either two particles or two
holes, the generalized Cooper equation in the IFG case has no real-energy
solutions. Rather, it possesses two complex-conjugate solutions with purely
imaginary energies. This implies that the IFG ground state is unstable when an
attractive interaction is switched on. However, solving the BS equation for the
BCS ground state reveals two types of {\it real} solutions: one describing
moving (i.e., having nonzero total, or center-of-mass, momenta) Cooper pairs as
resonances (or bound composite particles with a {\it finite} lifetime), and
another exhibiting superconducting collective excitations sometimes known as
Anderson-Bogoliubov-Higgs (ABH) modes. A Bose-Einstein-condensation-based
picture of superconductivity is addressed.Comment: 5 pages in PS, including 3 figures. In press Physica
Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs
Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta
(CMM) is studied with a set of renormalized equations assuming a short-ranged
(attractive) pairwise interfermion interaction. Expanding the associated
dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a
term {\it linear} in the CMM dominates the pair excitation energy, while the
quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies
prevails for any coupling {\it only} in the limit of zero Fermi velocity when
the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed
numerically. The linear term, moreover, exhibits CP breakup beyond a threshold
CMM value which vanishes with coupling. This makes all the excited
(nonzero-CMM) BE levels with preformed CPs collapse into a single ground level
so that a BCS condensate (where only zero CMM CPs are usually allowed) appears
in zero coupling to be a special case in either 2D or 3D of the BE condensate
of linear-dispersion-relation CPs.Comment: Four pages including four figures. To be published in Physica
Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors
A two-dimensional (2D) assembly of noninteracting, temperature-dependent,
pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions
is examined in a binary boson-fermion statistical model as the Bose-Einstein
condensation (BEC) singularity temperature is approached from above.
Compared with BCS theory (which is {\it not} a BEC theory) substantially higher
's are obtained without any adjustable parameters, that fall roughly
within the range of empirical 's for quasi-2D cuprate superconductors.Comment: 4 page
Statistical Model of Superconductivity in a 2D Binary Boson-Fermion Mixture
A two-dimensional (2D) assembly of noninteracting, temperature-dependent,
composite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with
unpaired fermions is examined in a binary boson-fermion statistical model as
the superconducting singularity temperature is approached from above. The model
is derived from {\it first principles} for the BCS model interfermion
interaction from three extrema of the system Helmholtz free energy (subject to
constant pairable-fermion number) with respect to: a) the pairable-fermion
distribution function; b) the number of excited (bosonic) CPs, i.e., with
nonzero total momenta--usually ignored in BCS theory--and with the appropriate
(linear, as opposed to quadratic) dispersion relation that arises from the
Fermi sea; and c) the number of CPs with zero total momenta. Compared with the
BCS theory condensate, higher singularity temperatures for the Bose-Einstein
condensate are obtained in the binary boson-fermion mixture model which are in
rough agreement with empirical critical temperatures for quasi-2D
superconductorsComment: 16 pages and 4 figures. This is a improved versio
Linear to quadratic crossover of Cooper pair dispersion relation
Cooper pairing is studied in three dimensions to determine its binding energy
for all coupling using a general separable interfermion interaction. Also
considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A
coupling-independent {\it linear} term in the CMM dominates the pair excitation
energy in weak coupling and/or high fermion density, while the more familiar
quadratic term prevails only in the extreme low-density (i.e., vacuum) limit
for any nonzero coupling. The linear-to-quadratic crossover of the CP
dispersion relation is analyzed numerically, and is expected to play a central
role in a model of superconductivity (and superfluidity) simultaneously
accommodating a BCS condensate as well as a Bose-Einstein condensate of CP
bosons.Comment: 13 pages plus 2 figure
Two-dimensional Bose-Einstein Condensation in Cuprate Superconductors
Transition temperatures calculated using the BCS model
electron-phonon interaction without any adjustable parameters agree with
empirical values for quasi-2D cuprate superconductors. They follow from a
two-dimensional gas of temperature-dependent Cooper pairs in chemical and
thermal equilibrium with unpaired fermions in a boson-fermion (BF) statistical
model as the Bose-Einstein condensation (BEC) singularity temperature is
approached from above. The {\it linear} (as opposed to quadratic) boson
dispersion relation due to the Fermi sea yields substantially higher 's
with the BF model than with BCS or pure-boson BEC theories.Comment: 7 pages including 2 figure
The inclusive jet cross section in p-bar p collisions at ?s = 1.8 TeV using the kT algorithm.
The central inclusive jet cross section has been measured using a successive-combination algorithm for reconstruction of jets. The measurement uses 87.3 pb−1 of data collected with the DØ detector at the Fermilab Tevatron Collider during 1994–1995. The cross section, reported as a function of transverse momentum (pT>60 GeV) in the central region of pseudorapidity (|η|<0.5), exhibits reasonable agreement with next-to-leading order QCD predictions, except at low pT where the agreement is marginal