660 research outputs found
An introduction to phase transitions in stochastic dynamical systems
We give an introduction to phase transitions in the steady states of systems
that evolve stochastically with equilibrium and nonequilibrium dynamics, the
latter defined as those that do not possess a time-reversal symmetry. We try as
much as possible to discuss both cases within the same conceptual framework,
focussing on dynamically attractive `peaks' in state space. A quantitative
characterisation of these peaks leads to expressions for the partition function
and free energy that extend from equilibrium steady states to their
nonequilibrium counterparts. We show that for certain classes of nonequilibrium
systems that have been exactly solved, these expressions provide precise
predictions of their macroscopic phase behaviour.Comment: Pedagogical talk contributed to the "Ageing and the Glass Transition"
Summer School, Luxembourg, September 2005. 12 pages, 8 figures, uses the IOP
'jpconf' document clas
Exact joint density-current probability function for the asymmetric exclusion process
We study the asymmetric exclusion process with open boundaries and derive the
exact form of the joint probability function for the occupation number and the
current through the system. We further consider the thermodynamic limit,
showing that the resulting distribution is non-Gaussian and that the density
fluctuations have a discontinuity at the continuous phase transition, while the
current fluctuations are continuous. The derivations are performed by using the
standard operator algebraic approach, and by the introduction of new operators
satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure
Single microwave photon detection in the micromaser
High efficiency single photon detection is an interesting problem for many
areas of physics, including low temperature measurement, quantum information
science and particle physics. For optical photons, there are many examples of
devices capable of detecting single photons with high efficiency. However
reliable single photon detection of microwaves is very difficult, principally
due to their low energy. In this paper we present the theory of a cascade
amplifier operating in the microwave regime that has an optimal quantum
efficiency of 93%. The device uses a microwave photon to trigger the stimulated
emission of a sequence of atoms where the energy transition is readily
detectable. A detailed description of the detector's operation and some
discussion of the potential limitations of the detector are presented.Comment: 8 pages, 5 figure
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
A dynamically extending exclusion process
An extension of the totally asymmetric exclusion process, which incorporates
a dynamically extending lattice is explored. Although originally inspired as a
model for filamentous fungal growth, here the dynamically extending exclusion
process (DEEP) is studied in its own right, as a nontrivial addition to the
class of nonequilibrium exclusion process models. Here we discuss various
mean-field approximation schemes and elucidate the steady state behaviour of
the model and its associated phase diagram. Of particular note is that the
dynamics of the extending lattice leads to a new region in the phase diagram in
which a shock discontinuity in the density travels forward with a velocity that
is lower than the velocity of the tip of the lattice. Thus in this region the
shock recedes from both boundaries.Comment: 20 pages, 12 figure
Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states
We examine stochastic processes that are used to model nonequilibrium
processes (e.g, pulling RNA or dragging colloids) and so deliberately violate
detailed balance. We argue that by combining an information-theoretic measure
of irreversibility with nonequilibrium work theorems, the thermal physics
implied by abstract dynamics can be determined. This measure is bounded above
by thermodynamic entropy production and so may quantify how well a stochastic
dynamics models reality. We also use our findings to critique various modeling
approaches and notions arising in steady-state thermodynamics.Comment: 8 pages, 2 figures, easy-to-read, single-column, large-print RevTeX4
format; version with modified abstract and additional discussion, references
to appear in Phys Rev Let
Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
We revisit the totally asymmetric simple exclusion process with open
boundaries (TASEP), focussing on the recent discovery by de Gier and Essler
that the model has a dynamical transition along a nontrivial line in the phase
diagram. This line coincides neither with any change in the steady-state
properties of the TASEP, nor the corresponding line predicted by domain wall
theory. We provide numerical evidence that the TASEP indeed has a dynamical
transition along the de Gier-Essler line, finding that the most convincing
evidence was obtained from Density Matrix Renormalisation Group (DMRG)
calculations. By contrast, we find that the dynamical transition is rather hard
to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss
in general terms scenarios that admit a distinction between static and dynamic
phase behaviour.Comment: 27 pages, 18 figures. v2 to appear in J Phys A features minor
corrections and better-quality figure
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