16,356 research outputs found
Nonlinear Schr\"odinger Equation for Superconductors
Using the Hartree-Fock-Bogoliubov factorization of the density matrix and the
Born-Oppenheimer approximation we show that the motion of the condensate
satisfies a nonlinear Schr\"odinger equation in the zero temperature limit. The
Galilean invariance of the equation is explicitly manifested. {}From this
equation some general properties of a superconductor, such as Josephson
effects, the Magnus force, and the Bogoliubov-Anderson mode can be obtained
readily.Comment: Latex, 12 page
Invalidity of Classes of Approximated Hall Effect Calculations
In this comment, I point out a number of approximated derivations for the
effective equation of motion, now been applied to d-wave superconductors by
Kopnin and Volovik are invalid. The major error in those approximated
derivations is the inappropriate use of the relaxation time approximation in
force-force correlation functions, or in force balance equations, or in similar
variations. This approximation is wrong and unnecessary.Comment: final version, minor changes, to appear in Phys. Rev. Let
Tunneling of a Quantized Vortex: Roles of Pinning and Dissipation
We have performed a theoretical study of the effects of pinning potential and
dissipation on vortex tunneling in superconductors. Analytical results are
obtained in various limits relevant to experiment. In general we have found
that pinning and dissipation tend to suppress the effect of the vortex velocity
dependent part of the Magnus force on vortex tunneling.Comment: Latex, 12 page
Effective one-component description of two-component Bose-Einstein condensate dynamics
We investigate dynamics in two-component Bose-Einstein condensates in the
context of coupled Gross-Pitaevskii equations and derive results for the
evolution of the total density fluctuations. Using these results, we show how,
in many cases of interest, the dynamics can be accurately described with an
effective one-component Gross-Pitaevskii equation for one of the components,
with the trap and interaction coefficients determined by the relative
differences in the scattering lengths. We discuss the model in various regimes,
where it predicts breathing excitations, and the formation of vector solitons.
An effective nonlinear evolution is predicted for some cases of current
experimental interest. We then apply the model to construct quasi-stationary
states of two-component condensates.Comment: 8 pages, 4 figure
Relic Abundances and the Boltzmann Equation
I discuss the validity of the quantum Boltzmann equation for the calculation
of WIMP relic densities.Comment: 5 pages, no figures; talk given at Dark Matter 2000; an important
reference is added in the revised versio
Internal Vortex Structure of a Trapped Spinor Bose-Einstein Condensate
The internal vortex structure of a trapped spin-1 Bose-Einstein condensate is
investigated. It is shown that it has a variety of configurations depending on,
in particular, the ratio of the relevant scattering lengths and the total
magnetization.Comment: replacement; minor grammatical corrections but with additional
figure
Microscopic theory of vortex dynamics in homogeneous superconductors
Vortex dynamics in fermionic superfluids is carefully considered from the
microscopic point of view. Finite temperatures, as well as impurities, are
explicitly incorporated. To enable readers understand the physical
implications, macroscopic demonstrations based on thermodynamics and
fluctuations- dissipation theorems are constructed. For the first time a clear
summary and a critical review of previous results are given.Comment: Presentations are made more straightforward. A detailed presentation
that why the vortex friction is finite when the geometric phase exists, as
required by referees, though I think it is obviou
Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function
From a logic point of view this is the third in the series to solve the
problem of absence of detailed balance. This paper will be denoted as SDS III.
The existence of a dynamical potential with both local and global meanings in
general nonequilibrium processes has been controversial. Following an earlier
explicit construction by one of us (Ao, J. Phys. {\bf A37}, L25 '04,
arXiv:0803.4356, referred to as SDS II), in the present paper we show
rigorously its existence for a generic class of situations in physical and
biological sciences. The local dynamical meaning of this potential function is
demonstrated via a special stochastic differential equation and its global
steady-state meaning via a novel and explicit form of Fokker-Planck equation,
the zero mass limit. We also give a procedure to obtain the special stochastic
differential equation for any given Fokker-Planck equation. No detailed balance
condition is required in our demonstration. For the first time we obtain here a
formula to describe the noise induced shift in drift force comparing to the
steady state distribution, a phenomenon extensively observed in numerical
studies. The comparison to two well known stochastic integration methods, Ito
and Stratonovich, are made ready. Such comparison was made elsewhere (Ao, Phys.
Life Rev. {\bf 2} (2005) 117. q-bio/0605020).Comment: latex. 13 page
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