10,273 research outputs found

### Cooper Instability in the Occupation Dependent Hopping Hamiltonians

A generic Hamiltonian, which incorporates the effect of the orbital
contraction on the hopping amplitude between the nearest sites, is studied both
analytically at the weak coupling limit and numerically at the intermediate and
strong coupling regimes for finite atomic cluster. The effect of the orbital
contraction due to hole localization at atomic sites is specified with two
coupling parameters V and W (multiplicative and additive contraction terms).
The singularity of the vertex part of the two-particle Green's function
determines the critical temperature Tc and the relaxation rate Gamma(T) of the
order parameter at temperature above Tc. Unlike in conventional BCS
superconductors, Gamma has a non-zero imaginary part which may influence the
fluctuation conductivity of superconductor above Tc. We compute the ground
state energy as a function of the particle number and magnetic flux through the
cluster, and show the existence of the parity gap Delta appearing at the range
of system parameters consistent with the appearance of Cooper instability.
Numeric calculation of the Hubbard model (with U>0) at arbitrary occupation
does not show any sign of superconductivity in small cluster.Comment: 13 pages, 12 figure

### Persistent Currents in Helical Structures

Recent discovery of mesoscopic electronic structures, in particular the
carbon nanotubes, made necessary an investigation of what effect may helical
symmetry of the conductor (metal or semiconductor) have on the persistent
current oscillations. We investigate persistent currents in helical structures
which are non-decaying in time, not requiring a voltage bias, dissipationless
stationary flow of electrons in a normal-metallic or semiconducting cylinder or
circular wire of mesoscopic dimension. In the presence of magnetic flux along
the toroidal structure, helical symmetry couples circular and longitudinal
currents to each other. Our calculations suggest that circular persistent
currents in these structures have two components with periods $\Phi_0$ and
$\Phi_0/s$ ($s$ is an integer specific to any geometry). However, resultant
circular persistent current oscillations have $\Phi_0$ period.
\pacs{PACS:}PACS:73.23.-bComment: 4 pages, 2 figures. Submitted to PR

### Spin Current in p-wave Superconducting Rings

A formula of the spin current in mesoscopic superconductors is derived from
the mean-field theory of superconductivity. The spin flow is generated by the
spatial fluctuations of $\vec{d}$ which represents a spin state of spin-triplet
superconductors. We discuss a possibility of the circulating spin current in
isolated p-wave superconducting rings at the zero magnetic field. The direction
of the spin current depends on topological numbers which characterize the
spatial configuration of $\vec{d}$ on the ring.Comment: 4page

### Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles

Conventional models of Josephson junction dynamics rely on the absence of low
energy quasiparticle states due to a large superconducting gap. With this
assumption the quasiparticle degrees of freedom become "frozen out" and the
phase difference becomes the only free variable, acting as a fictitious
particle in a local in time Josephson potential related to the adiabatic and
non-dissipative supercurrent across the junction. In this article we develop a
general framework to incorporate the effects of low energy quasiparticles
interacting non-adiabatically with the phase degree of freedom. Such
quasiparticle states exist generically in constriction type junctions with high
transparency channels or resonant states, as well as in junctions of
unconventional superconductors. Furthermore, recent experiments have revealed
the existence of spurious low energy in-gap states in tunnel junctions of
conventional superconductors - a system for which the adiabatic assumption
typically is assumed to hold. We show that the resonant interaction with such
low energy states rather than the Josephson potential defines nonlinear
Josephson dynamics at small amplitudes.Comment: 9 pages, 1 figur

### Nonparametric deconvolution problem for dependent sequences

We consider the nonparametric estimation of the density function of weakly
and strongly dependent processes with noisy observations. We show that in the
ordinary smooth case the optimal bandwidth choice can be influenced by long
range dependence, as opposite to the standard case, when no noise is present.
In particular, if the dependence is moderate the bandwidth, the rates of
mean-square convergence and, additionally, central limit theorem are the same
as in the i.i.d. case. If the dependence is strong enough, then the bandwidth
choice is influenced by the strength of dependence, which is different when
compared to the non-noisy case. Also, central limit theorem are influenced by
the strength of dependence. On the other hand, if the density is supersmooth,
then long range dependence has no effect at all on the optimal bandwidth
choice.Comment: Published in at http://dx.doi.org/10.1214/07-EJS154 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org

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