52 research outputs found
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise
We use the perturbative renormalization group to study classical stochastic
processes with memory. We focus on the generalized Langevin dynamics of the
\phi^4 Ginzburg-Landau model with additive noise, the correlations of which are
local in space but decay as a power-law with exponent \alpha in time. These
correlations are assumed to be due to the coupling to an equilibrium thermal
bath. We study both the equilibrium dynamics at the critical point and quenches
towards it, deriving the corresponding scaling forms and the associated
equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We
show that, while the first two retain their equilibrium values independently of
\alpha, the non-Markovian character of the dynamics affects the dynamic
exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial
dimensionality, N the number of components of the order parameter, and
\alpha_c(x,y) a function which we determine at second order in 4-D. We analyze
the dependence of the asymptotic fluctuation-dissipation ratio on various
parameters, including \alpha. We discuss the implications of our results for
several physical situations
Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
Within the universality class of ferromagnetic vector models with O(n)
symmetry and purely dissipative dynamics, we study the non-equilibrium critical
relaxation from a magnetized initial state. Transverse correlation and response
functions are exactly computed for Gaussian fluctuations and in the limit of
infinite number n of components of the order parameter. We find that the
fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes
differ already at the Gaussian level. In these two exactly solvable cases we
completely describe the crossover from the short-time to the long-time
behavior, corresponding to a disordered and a magnetized initial condition,
respectively. The effects of non-Gaussian fluctuations on longitudinal and
transverse quantities are calculated in the first order in the
epsilon-expansion and reliable three-dimensional estimates of the two FDRs are
obtained.Comment: 41 pages, 9 figure
Relaxation phenomena at criticality
The collective behaviour of statistical systems close to critical points is
characterized by an extremely slow dynamics which, in the thermodynamic limit,
eventually prevents them from relaxing to an equilibrium state after a change
in the thermodynamic control parameters. The non-equilibrium evolution
following this change displays some of the features typically observed in
glassy materials, such as ageing, and it can be monitored via dynamic
susceptibilities and correlation functions of the order parameter, the scaling
behaviour of which is characterized by universal exponents, scaling functions,
and amplitude ratios. This universality allows one to calculate these
quantities in suitable simplified models and field-theoretical methods are a
natural and viable approach for this analysis. In addition, if a statistical
system is spatially confined, universal Casimir-like forces acting on the
confining surfaces emerge and they build up in time when the temperature of the
system is tuned to its critical value. We review here some of the theoretical
results that have been obtained in recent years for universal quantities, such
as the fluctuation-dissipation ratio, associated with the non-equilibrium
critical dynamics, with particular focus on the Ising model with Glauber
dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting
in a film is discussed within the Gaussian model.Comment: Talk delivered at Statphys23, Genova, Italy, July 9-13, 2007. 8
pages, 7 figure
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
change
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
We study the time evolution of quantum one-dimensional gapless systems
evolving from initial states with a domain-wall. We generalize the
path-integral imaginary time approach that together with boundary conformal
field theory allows to derive the time and space dependence of general
correlation functions. The latter are explicitly obtained for the Ising
universality class, and the typical behavior of one- and two-point functions is
derived for the general case. Possible connections with the stochastic Loewner
evolution are discussed and explicit results for one-point time dependent
averages are obtained for generic \kappa for boundary conditions corresponding
to SLE. We use this set of results to predict the time evolution of the
entanglement entropy and obtain the universal constant shift due to the
presence of a domain wall in the initial state.Comment: 27 pages, 10 figure
Ageing in the contact process: Scaling behavior and universal features
We investigate some aspects of the ageing behavior observed in the contact
process after a quench from its active phase to the critical point. In
particular we discuss the scaling properties of the two-time response function
and we calculate it and its universal ratio to the two-time correlation
function up to first order in the field-theoretical epsilon-expansion. The
scaling form of the response function does not fit the prediction of the theory
of local scale invariance. Our findings are in good qualitative agreement with
recent numerical results.Comment: 20 pages, 3 figure
Aging at Criticality in Model C Dynamics
We study the off-equilibrium two-point critical response and correlation
functions for the relaxational dynamics with a coupling to a conserved density
(Model C) of the O(N) vector model. They are determined in an \epsilon=4-d
expansion for vanishing momentum. We briefly discuss their scaling behaviors
and the associated scaling forms are determined up to first order in epsilon.
The corresponding fluctuation-dissipation ratio has a non trivial large time
limit in the aging regime and, up to one-loop order, it is the same as that of
the Model A for the physically relevant case N=1. The comparison with
predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur
Entanglement negativity after a global quantum quench
We study the time evolution of the logarithmic negativity after a global quantum quench. In a 1+1-dimensional conformal invariant field theory, we consider the negativity between two intervals which can be either adjacent or disjoint. We show that the negativity follows the quasi-particle interpretation for the spreading of entanglement. We check and generalise our findings with a systematic analysis of the negativity after a quantum quench in the harmonic chain, highlighting two peculiar lattice effects: the late birth and the sudden death of entanglement
Is local scale invariance a generic property of ageing phenomena ?
In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J.
Phys. A 37, 10479] it is shown that the critical autoresponse function of the
1+1-dimensional contact process is not in agreement with the predictions of
local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques
- …