951 research outputs found
Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process
In the universality class of the one dimensional Kardar-Parisi-Zhang surface
growth, Derrida and Lebowitz conjectured the universality of not only the
scaling exponents, but of an entire scaling function. Since Derrida and
Lebowitz's original publication [PRL 80 209 (1998)] this universality has been
verified for a variety of continuous time, periodic boundary systems in the KPZ
universality class. Here, we present a numerical method for directly examining
the entire particle flux of the asymmetric exclusion process (ASEP), thus
providing an alternative to more difficult cumulant ratios studies. Using this
method, we find that the Derrida-Lebowitz scaling function (DLSF) properly
characterizes the large system size limit (N-->infty) of a single particle
discrete time system, even in the case of very small system sizes (N <= 22).
This fact allows us to not only verify that the DLSF properly characterizes
multiple particle discrete-time asymmetric exclusion processes, but also
provides a way to numerically solve for quantities of interest, such as the
particle hopping flux. This method can thus serve to further increase the ease
and accessibility of studies involving even more challenging dynamics, such as
the open boundary ASEP
A numerical approach to large deviations in continuous-time
We present an algorithm to evaluate the large deviation functions associated
to history-dependent observables. Instead of relying on a time discretisation
procedure to approximate the dynamics, we provide a direct continuous-time
algorithm, valuable for systems with multiple time scales, thus extending the
work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)).
The procedure is supplemented with a thermodynamic-integration scheme, which
improves its efficiency. We also show how the method can be used to probe large
deviation functions in systems with a dynamical phase transition -- revealed in
our context through the appearance of a non-analyticity in the large deviation
functions.Comment: Submitted to J. Stat. Mec
Non-Markovian generalization of the Lindblad theory of open quantum systems
A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.Comment: 10 pages, 1 figure, replaced by published versio
Irreversibility in a simple reversible model
This paper studies a parametrized family of familiar generalized baker maps,
viewed as simple models of time-reversible evolution. Mapping the unit square
onto itself, the maps are partly contracting and partly expanding, but they
preserve the global measure of the definition domain. They possess periodic
orbits of any period, and all maps of the set have attractors with well defined
structure. The explicit construction of the attractors is described and their
structure is studied in detail. There is a precise sense in which one can speak
about absolute age of a state, regardless of whether the latter is applied to a
single point, a set of points, or a distribution function. One can then view
the whole trajectory as a set of past, present and future states. This
viewpoint is then applied to show that it is impossible to define a priori
states with very large "negative age". Such states can be defined only a
posteriori. This gives precise sense to irreversibility -- or the "arrow of
time" -- in these time-reversible maps, and is suggested as an explanation of
the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure
Spatial structures and dynamics of kinetically constrained models for glasses
Kob and Andersen's simple lattice models for the dynamics of structural
glasses are analyzed. Although the particles have only hard core interactions,
the imposed constraint that they cannot move if surrounded by too many others
causes slow dynamics. On Bethe lattices a dynamical transition to a partially
frozen phase occurs. In finite dimensions there exist rare mobile elements that
destroy the transition. At low vacancy density, , the spacing, ,
between mobile elements diverges exponentially or faster in . Within the
mobile elements, the dynamics is intrinsically cooperative and the
characteristic time scale diverges faster than any power of (although
slower than ). The tagged-particle diffusion coefficient vanishes roughly
as .Comment: 4 pages. Accepted for pub. in Phys. Rev. Let
Fluctuations of the heat flux of a one-dimensional hard particle gas
Momentum-conserving one-dimensional models are known to exhibit anomalous
Fourier's law, with a thermal conductivity varying as a power law of the system
size. Here we measure, by numerical simulations, several cumulants of the heat
flux of a one-dimensional hard particle gas. We find that the cumulants, like
the conductivity, vary as power laws of the system size. Our results also
indicate that cumulants higher than the second follow different power laws when
one compares the ring geometry at equilibrium and the linear case in contact
with two heat baths (at equal or unequal temperatures). keywords: current
fluctuations, anomalous Fourier law, hard particle gasComment: 5 figure
Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
We consider the steady state of an open system in which there is a flux of
matter between two reservoirs at different chemical potentials. For a large
system of size , the probability of any macroscopic density profile
is ; thus generalizes to
nonequilibrium systems the notion of free energy density for equilibrium
systems. Our exact expression for is a nonlocal functional of ,
which yields the macroscopically long range correlations in the nonequilibrium
steady state previously predicted by fluctuating hydrodynamics and observed
experimentally.Comment: 4 pages, RevTeX. Changes: correct minor errors, add reference, minor
rewriting requested by editors and refere
Point force manipulation and activated dynamics of polymers adsorbed on structured substrates
We study the activated motion of adsorbed polymers which are driven over a
structured substrate by a localized point force.Our theory applies to
experiments with single polymers using, for example, tips of scanning force
microscopes to drag the polymer.We consider both flexible and semiflexible
polymers,and the lateral surface structure is represented by double-well or
periodic potentials. The dynamics is governed by kink-like excitations for
which we calculate shapes, energies, and critical point forces. Thermally
activated motion proceeds by the nucleation of a kink-antikink pair at the
point where the force is applied and subsequent diffusive separation of kink
and antikink. In the stationary state of the driven polymer, the collective
kink dynamics can be described by an one-dimensional symmetric simple exclusion
process.Comment: 7 pages, 2 Figure
Microscopic derivation of the Jaynes-Cummings model with cavity losses
In this paper we provide a microscopic derivation of the master equation for
the Jaynes-Cummings model with cavity losses. We single out both the
differences with the phenomenological master equation used in the literature
and the approximations under which the phenomenological model correctly
describes the dynamics of the atom-cavity system. Some examples wherein the
phenomenological and the microscopic master equations give rise to different
predictions are discussed in detail.Comment: 9 pages, 3 figures New version with minor correction Accepted for
publication on Physical Review
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