427 research outputs found
Semi-classical theory of magnetic quantum oscillations in a two-dimensional multiband canonical Fermi liquid
The semi-classical Lifshitz-Kosevich (LK) description of quantum oscillations
is extended to a multiband two-dimensional Fermi liquid with a constant number
of electrons. The amplitudes of novel oscillations with combination
frequencies, recently predicted and observed experimentally, are analytically
derived and compared with the single-band amplitudes. The combination
amplitudes decay with temperature exponentially faster than the standard
harmonics, and this provides a valuable tool for their experimental
identification.Comment: 3 pages, REVTeX 3.0, one eps-figure included in the tex
The weak localization for the alloy-type Anderson model on a cubic lattice
We consider alloy type random Schr\"odinger operators on a cubic lattice
whose randomness is generated by the sign-indefinite single-site potential. We
derive Anderson localization for this class of models in the Lifshitz tails
regime, i.e. when the coupling parameter is small, for the energies
.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy
Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns
We analyze a recent experiment of Sharon \textit{et al.} (2003) on the
coarsening, due to surface tension, of fractal viscous fingering patterns
(FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw
model, a natural model for that experiment, belongs to the same universality
class as model B of phase ordering. Two series of numerical simulations with
model B are performed, with the FVFPs grown in the experiment, and with
Diffusion Limited Aggregates, as the initial conditions. We observed
Lifshitz-Slyozov scaling at intermediate distances and very slow
convergence to this scaling at small distances. Dynamic scale invariance breaks
down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.
Phase diagram for unzipping DNA with long-range interactions
We present a critique and extension of the mean-field approach to the
mechanical pulling transition in bound polymer systems. Our model is motivated
by the theoretically and experimentally important examples of adsorbed polymers
and double-stranded DNA, and we focus on the case in which quenched disorder in
the sequence of monomers is unimportant for the statistical mechanics. We show
how including excluded volume interactions in the model affects the phase
diagram for the critical pulling force, and we predict a re-entrancy phase at
low temperatures which has not been previously discussed. We also consider the
case of non-equilibrium pulling, in which the external force probes the local,
rather than the global structure of the dsDNA or adsorbed polymer. The dynamics
of the pulling transition in such experiments could illuminate the polymer's
loop structure, which depends on the nature of excluded volume interactions.Comment: 4 pages, 2 figures; this version clarifies Eq. 8, and corrects errors
in Fig.
Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility
The coarsening dynamics of the Cahn-Hilliard equation with order-parameter
dependent mobility, , is addressed at
zero temperature in the Lifshitz-Slyozov limit where the minority phase
occupies a vanishingly small volume fraction. Despite the absence of bulk
diffusion for , the mean domain size is found to grow as , due to subdiffusive transport of the order parameter
through the majority phase. The domain-size distribution is determined
explicitly for the physically relevant case .Comment: 4 pages, Revtex, no figure
Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model
This paper describes the application of finite-size scaling concepts to
domain growth in systems with a non-conserved order parameter. A finite-size
scaling ansatz for the time-dependent order parameter distribution function is
proposed, and tested with extensive Monte-Carlo simulations of domain growth in
the 2-D spin-flip kinetic Ising model. The scaling properties of the
distribution functions serve to elucidate the configurational self-similarity
that underlies the dynamic scaling picture. Moreover, it is demonstrated that
the application of finite-size-scaling techniques facilitates the accurate
determination of the bulk growth exponent even in the presence of strong
finite-size effects, the scale and character of which are graphically exposed
by the order parameter distribution function. In addition it is found that one
commonly used measure of domain size--the scaled second moment of the
magnetisation distribution--belies the full extent of these finite-size
effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401
Resonant scattering on impurities in the Quantum Hall Effect
We develop a new approach to carrier transport between the edge states via
resonant scattering on impurities, which is applicable both for short and long
range impurities. A detailed analysis of resonant scattering on a single
impurity is performed. The results are used for study of the inter-edge
transport by multiple resonant hopping via different impurities' sites. It is
shown that the total conductance can be found from an effective Schroedinger
equation with constant diagonal matrix elements in the Hamiltonian, where the
complex non-diagonal matrix elements are the amplitudes of a carrier hopping
between different impurities. It is explicitly demonstrated how the complex
phase leads to Aharonov-Bohm oscillations in the total conductance. Neglecting
the contribution of self-crossing resonant-percolation trajectories, one finds
that the inter-edge carrier transport is similar to propagation in
one-dimensional system with off-diagonal disorder. We demonstrated that each
Landau band has an extended state , while all other states are
localized. The localization length behaves as .Comment: RevTex 41 pages; 3 Postscript figure on request; Final version
accepted for publication in Phys. Rev. B. A new section added contained a
comparison with other method
Quantum cavitation in liquid helium
Using a functional-integral approach, we have determined the temperature
below which cavitation in liquid helium is driven by thermally assisted quantum
tunneling. For both helium isotopes, we have obtained the crossover temperature
in the whole range of allowed negative p essures. Our results are compatible
with recent experimental results on 4He.Comment: Typeset using Revtex, 10 pages and 2 figures, Phys. Rev B (1996
Distribution of the area enclosed by a 2D random walk in a disordered medium
The asymptotic probability distribution for a Brownian particle wandering in
a 2D plane with random traps to enclose the algebraic area A by time t is
calculated using the instanton technique.Comment: 4 pages, ReVTeX. Phys. Rev. E (March 1999), to be publishe
Theory of Phase Ordering Kinetics
The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.Comment: To appear in Advances in Physics. 85 pages, latex, no figures. For a
hard copy with figures, email [email protected]
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