571 research outputs found
Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior
A model of an elastic manifold driven through a random medium by an applied
force F is studied focussing on the effects of inertia and elastic waves, in
particular {\it stress overshoots} in which motion of one segment of the
manifold causes a temporary stress on its neighboring segments in addition to
the static stress. Such stress overshoots decrease the critical force for
depinning and make the depinning transition hysteretic. We find that the steady
state velocity of the moving phase is nevertheless history independent and the
critical behavior as the force is decreased is in the same universality class
as in the absence of stress overshoots: the dissipative limit which has been
studied analytically. To reach this conclusion, finite-size scaling analyses of
a variety of quantities have been supplemented by heuristic arguments.
If the force is increased slowly from zero, the spectrum of avalanche sizes
that occurs appears to be quite different from the dissipative limit. After
stopping from the moving phase, the restarting involves both fractal and
bubble-like nucleation. Hysteresis loops can be understood in terms of a
depletion layer caused by the stress overshoots, but surprisingly, in the limit
of very large samples the hysteresis loops vanish. We argue that, although
there can be striking differences over a wide range of length scales, the
universality class governing this pseudohysteresis is again that of the
dissipative limit. Consequences of this picture for the statistics and dynamics
of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte
Avalanches and the Renormalization Group for Pinned Charge-Density Waves
The critical behavior of charge-density waves (CDWs) in the pinned phase is
studied for applied fields increasing toward the threshold field, using
recently developed renormalization group techniques and simulations of
automaton models. Despite the existence of many metastable states in the pinned
state of the CDW, the renormalization group treatment can be used successfully
to find the divergences in the polarization and the correlation length, and, to
first order in an expansion, the diverging time scale. The
automaton models studied are a charge-density wave model and a ``sandpile''
model with periodic boundary conditions; these models are found to have the
same critical behavior, associated with diverging avalanche sizes. The
numerical results for the polarization and the diverging length and time scales
in dimensions are in agreement with the analytical treatment. These
results clarify the connections between the behaviour above and below
threshold: the characteristic correlation lengths on both sides of the
transition diverge with different exponents. The scaling of the distribution of
avalanches on the approach to threshold is found to be different for automaton
and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS
files also available by anonymous ftp from external.nj.nec.com in directory
/pub/alan/cdwfigs
Creep motion in a random-field Ising model
We analyze numerically a moving interface in the random-field Ising model
which is driven by a magnetic field. Without thermal fluctuations the system
displays a depinning phase transition, i.e., the interface is pinned below a
certain critical value of the driving field. For finite temperatures the
interface moves even for driving fields below the critical value. In this
so-called creep regime the dependence of the interface velocity on the
temperature is expected to obey an Arrhenius law. We investigate the details of
this Arrhenius behavior in two and three dimensions and compare our results
with predictions obtained from renormalization group approaches.Comment: 6 pages, 11 figures, accepted for publication in Phys. Rev.
Effects of disorder on the wave front depinning transition in spatially discrete systems
Pinning and depinning of wave fronts are ubiquitous features of spatially
discrete systems describing a host of phenomena in physics, biology, etc. A
large class of discrete systems is described by overdamped chains of nonlinear
oscillators with nearest-neighbor coupling and subject to random external
forces. The presence of weak randomness shrinks the pinning interval and it
changes the critical exponent of the wave front depinning transition from 1/2
to 3/2. This effect is derived by means of a recent asymptotic theory of the
depinning transition, extended to discrete drift-diffusion models of transport
in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
Temperature and ac Effects on Charge Transport in Metallic Arrays of Dots
We investigate the effects of finite temperature, dc pulse, and ac drives on
the charge transport in metallic arrays using numerical simulations. For finite
temperatures there is a finite conduction threshold which decreases linearly
with temperature. Additionally we find a quadratic scaling of the
current-voltage curves which is independent of temperature for finite
thresholds. These results are in excellent agreement with recent experiments on
2D metallic dot arrays. We have also investigated the effects of an ac drive as
well as a suddenly applied dc drive. With an ac drive the conduction threshold
decreases for fixed frequency and increasing amplitude and saturates for fixed
amplitude and increasing frequency. For sudden applied dc drives below
threshold we observe a long time power law conduction decay.Comment: 6 pages, 7 postscript figure
Velocity-force characteristics of a driven interface in a disordered medium
Using a dynamic functional renormalization group treatment of driven elastic
interfaces in a disordered medium, we investigate several aspects of the
creep-type motion induced by external forces below the depinning threshold
: i) We show that in the experimentally important regime of forces
slightly below the velocity obeys an Arrhenius-type law
with an effective energy barrier
vanishing linearly when f approaches the threshold . ii) Thermal
fluctuations soften the pinning landscape at high temperatures. Determining the
corresponding velocity-force characteristics at low driving forces for internal
dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius
type creep involving the reduced threshold
force alone. For d=3 we obtain a similar v-f characteristic which is,
however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure
The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension
We investigate the depinning transition for driven interfaces in the
random-field Ising model for various dimensions. We consider the order
parameter as a function of the control parameter (driving field) and examine
the effect of thermal fluctuations. Although thermal fluctuations drive the
system away from criticality the order parameter obeys a certain scaling law
for sufficiently low temperatures and the corresponding exponents are
determined. Our results suggest that the so-called upper critical dimension of
the depinning transition is five and that the systems belongs to the
universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.
Crossover from 2-dimensional to 1-dimensional collective pinning in NbSe3
We have fabricated NbSe structures with widths comparable to the
Fukuyama-Lee-Rice phase-coherence length. For samples already in the
2-dimensional pinning limit, we observe a crossover from 2-dimensional to
1-dimensional collective pinning when the crystal width is less than 1.6
m, corresponding to the phase-coherence length in this direction. Our
results show that surface pinning is negligible in our samples, and provide a
means to probe the dynamics of single domains giving access to a new regime in
charge-density wave physics.Comment: 4 pages, 2 figures, and 1 table. Accepted for publication in Physical
Review
Mott insulators in strong electric fields
Recent experiments on ultracold atomic gases in an optical lattice potential
have produced a Mott insulating state of Rb atoms. This state is stable to a
small applied potential gradient (an `electric' field), but a resonant response
was observed when the potential energy drop per lattice spacing (E), was close
to the repulsive interaction energy (U) between two atoms in the same lattice
potential well. We identify all states which are resonantly coupled to the Mott
insulator for E close to U via an infinitesimal tunneling amplitude between
neighboring potential wells. The strong correlation between these states is
described by an effective Hamiltonian for the resonant subspace. This
Hamiltonian exhibits quantum phase transitions associated with an Ising density
wave order, and with the appearance of superfluidity in the directions
transverse to the electric field. We suggest that the observed resonant
response is related to these transitions, and propose experiments to directly
detect the order parameters. The generalizations to electric fields applied in
different directions, and to a variety of lattices, should allow study of
numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference
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