380 research outputs found
Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
We study analytically the probability distribution of the heat released by an
ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium
relaxation process following a temperature quench. We focus on the asymmetry
properties of the heat distribution in the nonstationary dynamics, in order to
study the forms taken by the Fluctuation Theorem as the number of degrees of
freedom is varied. After analysing in great detail the cases of one and two
oscillators, we consider the limit of a large number of oscillators, where the
behavior of fluctuations is enriched by a condensation transition with a
nontrivial phase diagram, characterized by reentrant behavior. Numerical
simulations confirm our analytical findings. We also discuss and highlight how
concepts borrowed from the study of fluctuations in equilibrium under symmetry
breaking conditions [Gaspard, J. Stat. Mech. P08021 (2012)] turn out to be
quite useful in understanding the deviations from the standard Fluctuation
Theorem.Comment: 16 pages, 7 figure
Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model
The evolution of the structure factor is studied during the phase-ordering
dynamics of the kinetic Ising model with conserved order parameter. A
preasymptotic multiscaling regime is found as in the solution of the
Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is
always approached through a crossover from multiscaling to standard scaling,
independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let
Energy and Heat Fluctuations in a Temperature Quench
Fluctuations of energy and heat are investigated during the relaxation
following the instantaneous temperature quench of an extended system. Results
are obtained analytically for the Gaussian model and for the large model
quenched below the critical temperature . The main finding is that
fluctuations exceeding a critical threshold do condense. Though driven by a
mechanism similar to that of Bose-Einstein condensation, this phenomenon is an
out-of-equilibrium feature produced by the breaking of energy equipartition
occurring in the transient regime. The dynamical nature of the transition is
illustrated by phase diagrams extending in the time direction.Comment: To be published in the Proceedings of the Research Program "Small
system non equilibrium fluctuations, dynamics and stochastics, and anomalous
behavior", Kavli Institute for Theoretical Physics China, July 2013. 40
pages, 9 figure
Off equilibrium response function in the one dimensional random field Ising model
A thorough numerical investigation of the slow dynamics in the d=1 random
field Ising model in the limit of an infinite ferromagnetic coupling is
presented. Crossovers from the preasymptotic pure regime to the asymptotic
Sinai regime are investigated for the average domain size, the autocorrelation
function and staggered magnetization. By switching on an additional small
random field at the time tw the linear off equilibrium response function is
obtained, which displays as well the crossover from the nontrivial behavior of
the d=1 pure Ising model to the asymptotic behavior where it vanishes
identically.Comment: 12 pages, 10 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
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation,
connecting the response of a generic observable to the appropriate correlation
functions, for Markov systems. The relation, which takes a similar form for
systems governed by a master equation or by a Langevin equation, can be derived
to every order, in large generality with respect to the considered model, in
equilibrium and out of equilibrium as well. On the basis of the fluctuation
dissipation relation we propose a particular response function, namely the
second order susceptibility of the two-particle correlation function, as an
effective quantity to detect and quantify cooperative effects in glasses and
disordered systems. We test this idea by numerical simulations of the
Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure
Two-vortex equilibrium in the flow past a flat plate at incidence
The two-dimensional inviscid incompressible steady flow past an inclined flat plate
is considered. A locus of asymmetric equilibrium configurations for vortex pairs
is detected. It is shown that the flat geometry has peculiar properties compared to
other geometries: (i) in order to satisfy the Kutta condition at both edges, which
ensures flow regularity, the total circulation and the force acting on the plate must be
zero; and (ii) the Kutta condition and the free vortex equilibrium conditions are not
independent of each other. The non-existence of symmetric equilibrium configurations
for an orthogonal plate is extended to more general asymmetric flows
The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach
We consider the N-vortex problem on a ellipsoid of revolution. Applying
standard techniques of classical perturbation theory we construct a sequence of
conformal transformations from the ellipsoid into the complex plane. Using
these transformations the equations of motion for the N-vortex problem on the
ellipsoid are written as a formal series on the eccentricity of the ellipsoid's
generating ellipse. First order equations are obtained explicitly. We show
numerically that the truncated first order system for the three-vortices system
on the symmetric ellipsoid is non-integrable.Comment: 14 pages, 1 figur
Generic features of the fluctuation dissipation relation in coarsening systems
The integrated response function in phase-ordering systems with scalar,
vector, conserved and non conserved order parameter is studied at various space
dimensionalities. Assuming scaling of the aging contribution we obtain, by numerical simulations
and analytical arguments, the phenomenological formula describing the
dimensionality dependence of in all cases considered. The primary
result is that vanishes continuously as approaches the lower
critical dimensionality . This implies that i) the existence of a non
trivial fluctuation dissipation relation and ii) the failure of the connection
between statics and dynamics are generic features of phase ordering at .Comment: 6 pages, 5 figure
Scaling and universality in the aging kinetics of the two-dimensional clock model
We study numerically the aging dynamics of the two-dimensional p-state clock
model after a quench from an infinite temperature to the ferromagnetic phase or
to the Kosterlitz-Thouless phase. The system exhibits the general scaling
behavior characteristic of non-disordered coarsening systems. For quenches to
the ferromagnetic phase, the value of the dynamical exponents, suggests that
the model belongs to the Ising-type universality class. Specifically, for the
integrated response function , we find
consistent with the value found in the two-dimensional
Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures
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