334 research outputs found
Topological quantization and degeneracy in Josephson-junction arrays
We consider the conductivity quantization in two-dimensional arrays of
mesoscopic Josephson junctions, and examine the associated degeneracy in
various regimes of the system. The filling factor of the system may be
controlled by the gate voltage as well as the magnetic field, and its
appropriate values for quantization is obtained by employing the Jain hierarchy
scheme both in the charge description and in the vortex description. The
duality between the two descriptions then suggests the possibility that the
system undergoes a change in degeneracy while the quantized conductivity
remains fixed.Comment: To appear in Phys. Rev.
A Renormalization-Group approach to the Coulomb Gap
The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.Comment: 16 pages, LaTeX. Diagrams available on request from
[email protected]. Changes to figure 4 and second half of section
Hall effect and geometric phases in Josephson junction arrays
Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect
Diabatic and Adiabatic Collective Motion in a Model Pairing System
Large amplitude collective motion is investigated for a model pairing
Hamiltonian containing an avoided level crossing. A classical theory of
collective motion for the adiabatic limit is applied utilising either a
time-dependent mean-field theory or a direct parametrisation of the
time-dependent Schr\"odinger equation. A modified local harmonic equation is
formulated to take account of the Nambu-Goldstone mode. It turns out that in
some cases the system selects a diabatic path. Requantizing the collective
Hamiltonian, a reasonable agreement with an exact calculation for the low-lying
levels are obtained for both weak and strong pairing force. This improves on
results of the conventional Born-Oppenheimer approximation.Comment: 23 pages, 7 ps figures. Latex, uses revtex and graphic
Duality and integer quantum Hall effect in isotropic 3D crystals
We show here a series of energy gaps as in Hofstadter's butterfly, which have
been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for
anisotropic three-dimensional (3D) periodic systems in magnetic fields
\Vec{B}, also arise in the isotropic case unless \Vec{B} points in
high-symmetry directions. Accompanying integer quantum Hall conductivities
can, surprisingly, take values
even for a fixed direction of \Vec{B}
unlike in the anisotropic case. We can intuitively explain the high-magnetic
field spectra and the 3D QHE in terms of quantum mechanical hopping by
introducing a ``duality'', which connects the 3D system in a strong \Vec{B}
with another problem in a weak magnetic field .Comment: 7 pages, 6 figure
Extension of random-phase approximation preserving energy weighted sum rules: an application to a 3-level Lipkin model
A limitation common to all extensions of random-phase approximation including
only particle-hole configurations is that they violate to some extent the
energy weighted sum rules. Considering one such extension, the improved RPA
(IRPA), already used to study the electronic properties of metallic clusters,
we show how it can be generalized in order to eliminate this drawback. This is
achieved by enlarging the configuration space, including also elementary
excitations corresponding to the annihilation of a particle (hole) and the
creation of another particle (hole) on the correlated ground state. The
approach is tested within a solvable 3-level model.Comment: 2 figure
Elimination of spurious states in the quasiparticle time blocking approximation
The quasiparticle time blocking approximation (QTBA) is considered as a model
for the description of excitations in open-shell nuclei. The QTBA is an
extension of the quasiparticle random phase approximation that includes
quasiparticle-phonon coupling. In the present version of the QTBA, the pairing
correlations are included within the framework of the BCS approximation. Thus,
in this model, the spurious states appear, which are caused by the
breaking of the symmetry related to the particle-number conservation. In this
work, the method is described which solves the problem of the spurious
states in the QTBA with the help of the projection technique. The method is
illustrated by calculations of excitations in Sn nucleus.Comment: 12 pages, 3 figures - To appear in the proceedings of the 59-th
International Meeting on Nuclear Spectroscopy and Nuclear Structure, June
15-19, 2009, Cheboksary, Russi
Low density expansion for Lyapunov exponents
In some quasi-one-dimensional weakly disordered media, impurities are large
and rare rather than small and dense. For an Anderson model with a low density
of strong impurities, a perturbation theory in the impurity density is
developed for the Lyapunov exponent and the density of states. The Lyapunov
exponent grows linearly with the density. Anomalies of the Kappus-Wegner type
appear for all rational quasi-momenta even in lowest order perturbation theory
Exact Eigenfunctions of -Body system with Quadratic Pair Potential
We obtain all the exact eigenvalues and the corresponding eigenfunctions of
-body Bose and Fermi systems with Quadratic Pair Potentials in one
dimension. The originally existed first excited state level is missing in one
dimension, which results from the operation of symmetry or antisymmetry of
identical particles. In two and higher dimensions, we give all the eigenvalues
and the analytical ground state wave functions and the number of degeneracy.
Through the comparison with Avinash Khare's results, we have perfected his
results.Comment: 7 pages,1 figur
Adiabatic response for Lindblad dynamics
We study the adiabatic response of open systems governed by Lindblad
evolutions. In such systems, there is an ambiguity in the assignment of
observables to fluxes (rates) such as velocities and currents. For the
appropriate notion of flux, the formulas for the transport coefficients are
simple and explicit and are governed by the parallel transport on the manifold
of instantaneous stationary states. Among our results we show that the response
coefficients of open systems, whose stationary states are projections, is given
by the adiabatic curvature.Comment: 33 pages, 4 figures, accepted versio
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