680 research outputs found
Quantum States Allowing Minimum Uncertainty Product of angular position and momentum
We provide necessary and sufficient conditions for states to have an
arbitrarily small uncertainty product of the azimuthal angle and its
canonical moment . We illustrate our results with analytical examples
The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree
Some results on the two-point function and on the analytic structure of the
momenta of the effective fugacity at the origin for a class of diluted
ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page
Nonlinear Hydrodynamics of Disentangled Flux-Line Liquids
In this paper we use non-Gaussian hydrodynamics to study the magnetic
response of a flux-line liquid in the mixed state of a type-II superconductor.
Both the derivation of our model, which goes beyond conventional Gaussian flux
liquid hydrodynamics, and its relationship to other approaches used in the
literature are discussed. We focus on the response to a transverse tilting
field which is controlled by the tilt modulus, c44, of the flux array. We show
that interaction effects can enhance c44 even in infinitely thick clean
materials. This enhancement can be interpreted as the appearance of a
disentangled flux-liquid fraction. In contrast to earlier work, our theory
incorporates the nonlocality of the intervortex interaction in the field
direction. This nonlocality is crucial for obtaining a nonvanishing
renormalization of the tilt modulus in the thermodynamic limit of thick
samples.Comment: 20 pages, 3 figures (submitted to PRB
Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models
We consider independent edge percolation models on Z, with edge occupation
probabilities p_ = p if |x-y| = 1, 1 - exp{- beta / |x-y|^2} otherwise. We
prove that oriented percolation occurs when beta > 1 provided p is chosen
sufficiently close to 1, answering a question posed in [Commun. Math. Phys.
104, 547 (1986)]. The proof is based on multi-scale analysis.Comment: 19 pages, 2 figures. See also Commentary on J. Stat. Phys. 150,
804-805 (2013), DOI 10.1007/s10955-013-0702-
Asymptotic integral kernel for ensembles of random normal matrices with radial potentials
We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-NSigma_{i=1}^{N}V_{alpha}(z_{i})} Pi_{1leqi<jleqN}|z_{i}-z_{j}|^{2} where V_{alpha}(z)=|z|^{alpha}, z in C and alpha in ]0,infty[. Asymptotic analysis with error estimates are obtained. A corollary of this expansion is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal--Bargmann space
Weak point disorder in strongly fluctuating flux-line liquids
We consider the effect of weak uncorrelated quenched disorder (point defects)
on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which
is based on mapping the flux-line system onto a quantum liquid of relativistic
charged bosons in 2+1 dimensions [P. Benetatos and M. C. Marchetti, Phys. Rev.
B 64, 054518, (2001)]. In this model, flux lines are allowed to be arbitrarily
curved and can even form closed loops. Point defects can be scalar or polar. In
the latter case, the direction of their dipole moments can be random or
correlated. Within the Gaussian approximation of our hydrodynamic model, we
calculate disorder-induced corrections to the correlation functions of the
flux-line fields and the elastic moduli of the flux-line liquid. We find that
scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease
the tilt modulus.Comment: 15 pages, submitted to Pramana-Journal of Physics for the special
volume on Vortex State Studie
Vortex Line Fluctuations in Model High Temperature Superconductors
We carry out Monte Carlo simulations of the uniformly frustrated 3d XY model
as a model for vortex line fluctuations in a high Tc superconductor. A density
of vortex lines of f=1/25 is considered. We find two sharp phase transitions.
The low T phase is an ordered vortex line lattice. The high T normal phase is a
vortex line liquid with much entangling, cutting, and loop excitations. An
intermediate phase is found which is characterized as a vortex line liquid of
disentangled lines. In this phase, the system displays superconducting
properties in the direction parallel to the magnetic field, but normal behavior
in planes perpendicular to the magnetic field.Comment: 38 pages, LaTeX 15 figures (upon request to
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