297 research outputs found
The Ginzburg-Landau theory in application
A numerical approach to Ginzburg-Landau (GL) theory is demonstrated and we
review its applications to several examples of current interest in the research
on superconductivity. This analysis also shows the applicability of the
two-dimensional approach to thin superconductors and the re-defined effective
GL parameter kappa. For two-gap superconductors, the conveniently written GL
equations directly show that the magnetic behavior of the sample depends not
just on the GL parameter of two bands, but also on the ratio of respective
coherence lengths.Comment: To be published in Physica C, VORTEX VI Conference Proceeding
Adiabatic theorems for generators of contracting evolutions
We develop an adiabatic theory for generators of contracting evolution on
Banach spaces. This provides a uniform framework for a host of adiabatic
theorems ranging from unitary quantum evolutions through quantum evolutions of
open systems generated by Lindbladians all the way to classically driven
stochastic systems. In all these cases the adiabatic evolution approximates, to
lowest order, the natural notion of parallel transport in the manifold of
instantaneous stationary states. The dynamics in the manifold of instantaneous
stationary states and transversal to it have distinct characteristics: The
former is irreversible and the latter is transient in a sense that we explain.
Both the gapped and gapless cases are considered. Some applications are
discussed.Comment: 31 pages, 4 figures, replaced by the version accepted for publication
in CM
General Adiabatic Evolution with a Gap Condition
We consider the adiabatic regime of two parameters evolution semigroups
generated by linear operators that are analytic in time and satisfy the
following gap condition for all times: the spectrum of the generator consists
in finitely many isolated eigenvalues of finite algebraic multiplicity, away
from the rest of the spectrum. The restriction of the generator to the spectral
subspace corresponding to the distinguished eigenvalues is not assumed to be
diagonalizable. The presence of eigenilpotents in the spectral decomposition of
the generator forbids the evolution to follow the instantaneous eigenprojectors
of the generator in the adiabatic limit. Making use of superadiabatic
renormalization, we construct a different set of time-dependent projectors,
close to the instantaneous eigeprojectors of the generator in the adiabatic
limit, and an approximation of the evolution semigroup which intertwines
exactly between the values of these projectors at the initial and final times.
Hence, the evolution semigroup follows the constructed set of projectors in the
adiabatic regime, modulo error terms we control
Global well-posedness for the KP-I equation on the background of a non localized solution
We prove that the Cauchy problem for the KP-I equation is globally well-posed
for initial data which are localized perturbations (of arbitrary size) of a
non-localized (i.e. not decaying in all directions) traveling wave solution
(e.g. the KdV line solitary wave or the Zaitsev solitary waves which are
localized in and periodic or conversely)
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
Superconducting Wigner Vortex Molecule near a Magnetic Disk
Within the non-linear Ginzburg-Landau (GL) theory, we investigate the vortex
structure in a superconducting thin film with a ferromagnetic disk on top of
it. Antivortices are stabilized in shells around a central core of vortices (or
a giant-vortex) with size-magnetization controlled ``magic numbers''. An
equilibrium vortex phase diagram is constructed. The transition between the
different vortex phases occurs through the creation of a vortex-antivortex pair
under the magnetic disk edge.Comment: 4 pages, 4 figures. Submitted to Phys. Rev. Let
Surprises in the Orbital Magnetic Moment and g-Factor of the Dynamic Jahn-Teller Ion C_{60}^-
We calculate the magnetic susceptibility and g-factor of the isolated
C_{60}^- ion at zero temperature, with a proper treatment of the dynamical
Jahn-Teller effect, and of the associated orbital angular momentum, Ham-reduced
gyromagnetic ratio, and molecular spin-orbit coupling. A number of surprises
emerge. First, the predicted molecular spin-orbit splitting is two orders of
magnitude smaller than in the bare carbon atom, due to the large radius of
curvature of the molecule. Second, this reduced spin-orbit splitting is
comparable to Zeeman energies, for instance, in X-band EPR at 3.39KGauss, and a
field dependence of the g-factor is predicted. Third, the orbital gyromagnetic
factor is strongly reduced by vibron coupling, and so therefore are the
effective weak-field g-factors of all low-lying states. In particular, the
ground-state doublet of C_{60}^- is predicted to show a negative g-factor of
\sim -0.1.Comment: 19 pages RevTex, 2 postscript figures include
Correlations Between Charge Ordering and Local Magnetic Fields in Overdoped YBaCuO
Zero-field muon spin relaxation (ZF-SR) measurements were undertaken on
under- and overdoped samples of superconducting YBaCuO to
determine the origin of the weak static magnetism recently reported in this
system. The temperature dependence of the muon spin relaxation rate in
overdoped crystals displays an unusual behavior in the superconducting state. A
comparison to the results of NQR and lattice structure experiments on highly
doped samples provides compelling evidence for strong coupling of charge, spin
and structural inhomogeneities.Comment: 4 pages, 4 figures, new data, new figures and modified tex
Pairing and Density Correlations of Stripe Electrons in a Two-Dimensional Antiferromagnet
We study a one-dimensional electron liquid embedded in a 2D antiferromagnetic
insulator, and coupled to it via a weak antiferromagnetic spin exchange
interaction. We argue that this model may qualitatively capture the physics of
a single charge stripe in the cuprates on length- and time scales shorter than
those set by its fluctuation dynamics. Using a local mean-field approach we
identify the low-energy effective theory that describes the electronic spin
sector of the stripe as that of a sine-Gordon model. We determine its phases
via a perturbative renormalization group analysis. For realistic values of the
model parameters we obtain a phase characterized by enhanced spin density and
composite charge density wave correlations, coexisting with subleading triplet
and composite singlet pairing correlations. This result is shown to be
independent of the spatial orientation of the stripe on the square lattice.
Slow transverse fluctuations of the stripes tend to suppress the density
correlations, thus promoting the pairing instabilities. The largest amplitudes
for the composite instabilities appear when the stripe forms an antiphase
domain wall in the antiferromagnet. For twisted spin alignments the amplitudes
decrease and leave room for a new type of composite pairing correlation,
breaking parity but preserving time reversal symmetry.Comment: Revtex, 28 pages incl. 5 figure
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change
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