985 research outputs found
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
Electron - nuclear recoil discrimination by pulse shape analysis
In the framework of the ``ULTIMA'' project, we use ultra cold superfluid 3He
bolometers for the direct detection of single particle events, aimed for a
future use as a dark matter detector. One parameter of the pulse shape observed
after such an event is the thermalization time constant. Until now it was
believed that this parameter only depends on geometrical factors and superfluid
3He properties, and that it is independent of the nature of the incident
particles. In this report we show new results which demonstrate that a
difference for muon- and neutron events, as well as events simulated by heater
pulses exist. The possibility to use this difference for event discrimination
in a future dark matter detector will be discussed.Comment: Proseedings of QFS 2007, Kazan, Russia; 8 pages, 4 figures. Submited
to J. Low Temp. Phy
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
Coupled Ripplon-Plasmon Modes in a Multielectron Bubble
In multielectron bubbles, the electrons form an effectively two-dimensional
layer at the inner surface of the bubble in helium. The modes of oscillation of
the bubble surface (the ripplons) are influenced by the charge redistribution
of the electrons along the surface. The dispersion relation for these charge
redistribution modes (`longitudinal plasmons') is derived and the coupling of
these modes to the ripplons is analysed. We find that the ripplon-plasmon
coupling in a multielectron bubble differs markedly from that of electrons a
flat helium surface. An equation is presented relating the spherical harmonic
components of the charge redistribution to those of the shape deformation of
the bubble.Comment: 8 pages, 1 figure, E-mail addresses: [email protected],
[email protected], [email protected], [email protected]
Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift
We obtain exact asymptotic results for the disorder averaged persistence of a
Brownian particle moving in a biased Sinai landscape. We employ a new method
that maps the problem of computing the persistence to the problem of finding
the energy spectrum of a single particle quantum Hamiltonian, which can be
subsequently found. Our method allows us analytical access to arbitrary values
of the drift (bias), thus going beyond the previous methods which provide
results only in the limit of vanishing drift. We show that on varying the
drift, the persistence displays a variety of rich asymptotic behaviors
including, in particular, interesting qualitative changes at some special
values of the drift.Comment: 17 pages, two eps figures (included
Persistence in a Stationary Time-series
We study the persistence in a class of continuous stochastic processes that
are stationary only under integer shifts of time. We show that under certain
conditions, the persistence of such a continuous process reduces to the
persistence of a corresponding discrete sequence obtained from the measurement
of the process only at integer times. We then construct a specific sequence for
which the persistence can be computed even though the sequence is
non-Markovian. We show that this may be considered as a limiting case of
persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte
Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
Non-equilibrium dynamics of classical random Ising spin chains are studied
using asymptotically exact real space renormalization group. Specifically the
random field Ising model with and without an applied field (and the Ising spin
glass (SG) in a field), in the universal regime of a large Imry Ma length so
that coarsening of domains after a quench occurs over large scales. Two types
of domain walls diffuse in opposite Sinai random potentials and mutually
annihilate. The domain walls converge rapidly to a set of system-specific
time-dependent positions {\it independent of the initial conditions}. We obtain
the time dependent energy, magnetization and domain size distribution
(statistically independent). The equilibrium limits agree with known exact
results. We obtain exact scaling forms for two-point equal time correlation and
two-time autocorrelations. We also compute the persistence properties of a
single spin, of local magnetization, and of domains. The analogous quantities
for the spin glass are obtained. We compute the two-point two-time correlation
which can be measured by experiments on spin-glass like systems. Thermal
fluctuations are found to be dominated by rare events; all moments of truncated
correlations are computed. The response to a small field applied after waiting
time , as measured in aging experiments, and the fluctuation-dissipation
ratio are computed. For ,
, it equals its equilibrium value X=1, though time
translational invariance fails. It exhibits for aging regime
with non-trivial , different from mean field.Comment: 55 pages, 9 figures, revte
Persistence of a particle in the Matheron-de Marsily velocity field
We show that the longitudinal position of a particle in a
-dimensional layered random velocity field (the Matheron-de Marsily
model) can be identified as a fractional Brownian motion (fBm) characterized by
a variable Hurst exponent for . The
fBm becomes marginal at . Moreover, using the known first-passage
properties of fBm we prove analytically that the disorder averaged persistence
(the probability of no zero crossing of the process upto time ) has a
power law decay for large with an exponent for and
for (with logarithmic correction at ), results that
were earlier derived by Redner based on heuristic arguments and supported by
numerical simulations (S. Redner, Phys. Rev. E {\bf 56}, 4967 (1997)).Comment: 4 pages Revtex, 1 .eps figure included, to appear in PRE Rapid
Communicatio
Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process
The percolation phase transitions of two-dimensional lattice networks under a
generalized Achlioptas process (GAP) are investigated. During the GAP, two
edges are chosen randomly from the lattice and the edge with minimum product of
the two connecting cluster sizes is taken as the next occupied bond with a
probability . At , the GAP becomes the random growth model and leads
to the minority product rule at . Using the finite-size scaling analysis,
we find that the percolation phase transitions of these systems with are always continuous and their critical exponents depend on .
Therefore, the universality class of the critical phenomena in two-dimensional
lattice networks under the GAP is related to the probability parameter in
addition.Comment: 7 pages, 14 figures, accepted for publication in Eur. Phys. J.
Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation
The persistence probability, , of a cluster to remain unaggregated is
studied in cluster-cluster aggregation, when the diffusion coefficient of a
cluster depends on its size as . In the mean-field the
problem maps to the survival of three annihilating random walkers with
time-dependent noise correlations. For the motion of persistent
clusters becomes asymptotically irrelevant and the mean-field theory provides a
correct description. For the spatial fluctuations remain relevant
and the persistence probability is overestimated by the random walk theory. The
decay of persistence determines the small size tail of the cluster size
distribution. For the distribution is flat and, surprisingly,
independent of .Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.
- …