436,835 research outputs found
Criticality and entanglement in random quantum systems
We review studies of entanglement entropy in systems with quenched
randomness, concentrating on universal behavior at strongly random quantum
critical points. The disorder-averaged entanglement entropy provides insight
into the quantum criticality of these systems and an understanding of their
relationship to non-random ("pure") quantum criticality. The entanglement near
many such critical points in one dimension shows a logarithmic divergence in
subsystem size, similar to that in the pure case but with a different universal
coefficient. Such universal coefficients are examples of universal critical
amplitudes in a random system. Possible measurements are reviewed along with
the one-particle entanglement scaling at certain Anderson localization
transitions. We also comment briefly on higher dimensions and challenges for
the future.Comment: Review article for the special issue "Entanglement entropy in
extended systems" in J. Phys.
Spinodal Phase Separation in Liquid Films with Quenched Disorder
We study spinodal phase separation in unstable thin liquid films on
chemically disordered substrates via simulations of the thin-film equation. The
disorder is characterized by immobile patches of varying size and Hamaker
constant. The effect of disorder is pronounced in the early stages
(amplification of fluctuations), remains during the intermediate stages and
vanishes in the late stages (domain growth). These findings are in contrast to
the well-known effects of quenched disorder in usual phase-separation
processes, viz., the early stages remain undisturbed and domain growth is
slowed down in the asymptotic regime. We also address the inverse problem of
estimating disorder by thin-film experiments.Comment: 12 pages, 7 figure
Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
We present comprehensive numerical results for domain growth in the
two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber
kinetics. We characterize the evolution via the {\it domain growth law}, and
two-time quantities like the {\it autocorrelation function} and {\it
autoresponse function}. Our results clearly establish that the growth law shows
a crossover from a pre-asymptotic regime with "power-law growth with a
disorder-dependent exponent" to an asymptotic regime with "logarithmic growth".
We compare this behavior with previous results on one-dimensional disordered
systems and we propose a unifying picture in a renormalization group framework.
We also study the corresponding crossover in the scaling functions for the
two-time quantities. Super-universality is found not to hold. Clear evidence
supporting the dimensionality dependence of the scaling exponent of the
autoresponse function is obtained.Comment: Thoroughly revised manuscript. The Introduction, Section 2 and
Section 4 have been largely rewritten. References added. Final version
accepted for publication on Journal of Statistical Mechanics: Theory and
Experimen
Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
We present a combination of heuristic and rigorous arguments indicating that
both the pure state structure and the overlap structure of realistic spin
glasses should be relatively simple: in a large finite volume with
coupling-independent boundary conditions, such as periodic, at most a pair of
flip-related (or the appropriate number of symmetry-related in the non-Ising
case) states appear, and the Parisi overlap distribution correspondingly
exhibits at most a pair of delta-functions at plus/minus the self-overlap. This
rules out the nonstandard SK picture introduced by us earlier, and when
combined with our previous elimination of more standard versions of the mean
field picture, argues against the possibility of even limited versions of mean
field ordering in realistic spin glasses. If broken spin flip symmetry should
occur, this leaves open two main possibilities for ordering in the spin glass
phase: the droplet/scaling two-state picture, and the chaotic pairs many-state
picture introduced by us earlier. We present scaling arguments which provide a
possible physical basis for the latter picture, and discuss possible reasons
behind numerical observations of more complicated overlap structures in finite
volumes.Comment: 22 pages (LaTeX; needs revtex), 1 figure (PostScript); to appear in
Physical Review
A FRAP model to investigate reaction-diffusion of proteins within a bounded domain: a theoretical approach
Temporally and spatially resolved measurements of protein transport inside
cells provide important clues to the functional architecture and dynamics of
biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique
has been used over the past three decades to measure the mobility of
macromolecules and protein transport and interaction with immobile structures
inside the cell nucleus. A theoretical model is presented that aims to describe
protein transport inside the nucleus, a process which is influenced by the
presence of a boundary (i.e. membrane). A set of reaction-diffusion equations
is employed to model both the diffusion of proteins and their interaction with
immobile binding sites. The proposed model has been designed to be applied to
biological samples with a Confocal Laser Scanning Microscope (CLSM) equipped
with the feature to bleach regions characterised by a scanning beam that has a
radially Gaussian distributed profile. The proposed model leads to FRAP curves
that depend on the on- and off-rates. Semi-analytical expressions are used to
define the boundaries of on- (off-) rate parameter space in simplified cases
when molecules move within a bounded domain. The theoretical model can be used
in conjunction to experimental data acquired by CLSM to investigate the
biophysical properties of proteins in living cells.Comment: 25 pages. Abstracts Proceedings, The American Society for Cell
Biology, 46th Annual Meeting, December 9-13, 2006, San Dieg
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
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