5,375 research outputs found
Absence of Cooper-type bound states in three- and few-electron systems
It is shown that the appearance of a fixed-point singularity in the kernel of
the two-electron Cooper problem is responsible for the formation of the Cooper
pair for an arbitrarily weak attractive interaction between two electrons. This
singularity is absent in the problem of three and few superconducting electrons
at zero temperature on the full Fermi sea. Consequently, such three- and
few-electron systems on the full Fermi sea do not form Cooper-type bound states
for an arbitrarily weak attractive pair interaction.Comment: 10 pages. Accepted in European Physical Journal
Relativistic three-particle dynamical equations: I. Theoretical development
Starting from the two-particle Bethe-Salpeter equation in the ladder
approximation and integrating over the time component of momentum, we rederive
three dimensional scattering integral equations satisfying constraints of
relativistic unitarity and covariance, first derived by Weinberg and by
Blankenbecler and Sugar. These two-particle equations are shown to be related
by a transformation of variables. Hence we show how to perform and relate
identical dynamical calculation using these two equations. Similarly, starting
from the Bethe-Salpeter-Faddeev equation for the three-particle system and
integrating over the time component of momentum, we derive several three
dimensional three-particle scattering equations satisfying constraints of
relativistic unitarity and covariance. We relate two of these three-particle
equations by a transformation of variables as in the two-particle case. The
three-particle equations we derive are very practical and suitable for
performing relativistic scattering calculations.Comment: 30 pages, Report # IFT P.070/93, [Text in Latex, e-mail:
[email protected] ; FAX: 55-11-288-8224
Dynamics of gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice
We suggest and study the stable disk- and cigar-shaped gap solitons of a
dipolar Bose-Einstein condensate of Cr atoms localized in the lowest
band gap by three optical-lattice (OL) potentials along orthogonal directions.
The one-dimensional version of these solitons of experimental interest confined
by an OL along the dipole moment direction and harmonic traps in transverse
directions is also considered. Important dynamics of (i) breathing oscillation
of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a
moving lattice along axial direction demonstrates the stability of gap
solitons. A movie clip of dragging of three-dimensional gap soliton is
included.Comment: To see the dragging movie clip please download sourc
NeutronC scattering near an Efimov state
The low-energy neutronC scattering in a neutron-neutron-core model is
studied with large scattering lengths near the conditions for the appearance of
an Efimov state. We show that the real part of the elastic wave phase-shift
() presents a zero, or a pole in , when the
system has an Efimov excited or virtual state. More precisely the pole scales
with the energy of the Efimov state (bound or virtual). We perform calculations
in the limit of large scattering lengths, disregarding the interaction range,
within a renormalized zero-range approach using subtracted equations. It is
also presented a brief discussion of these findings in the context of ultracold
atom physics with tunable scattering lengths
Quantum scattering in one dimension
A self-contained discussion of nonrelativistic quantum scattering is
presented in the case of central potentials in one space dimension, which will
facilitate the understanding of the more complex scattering theory in two and
three dimensions. The present discussion illustrates in a simple way the
concept of partial-wave decomposition, phase shift, optical theorem and
effective-range expansion.Comment: 8 page
Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture
Employing a time-dependent mean-field-hydrodynamic model we study the
generation of black solitons in a degenerate fermion-fermion mixture in a
cigar-shaped geometry using variational and numerical solutions. The black
soliton is found to be the first stationary vibrational excitation of the
system and is considered to be a nonlinear continuation of the vibrational
excitation of the harmonic oscillator state. We illustrate the stationary
nature of the black soliton, by studying different perturbations on it after
its formation.Comment: 7 pages, 10 figure
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