650 research outputs found
Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux
We consider the asymmetric simple exclusion processes (ASEP) on a ring
constrained to produce an atypically large flux, or an extreme activity. Using
quantum free fermion techniques we find the time-dependent conditional
transition probabilities and the exact dynamical structure factor under such
conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling
form. This gives a direct proof that the dynamical exponent in the extreme
current regime is rather than the KPZ exponent which
characterizes the ASEP in the regime of typical currents. Some of our results
extend to the activity in the partially asymmetric simple exclusion process,
including the symmetric case.Comment: 16 pages, 2 figure
Solution of the Lindblad equation for spin helix states
Using Lindblad dynamics we study quantum spin systems with dissipative
boundary dynamics that generate a stationary nonequilibrium state with a
non-vanishing spin current that is locally conserved except at the boundaries.
We demonstrate that with suitably chosen boundary target states one can solve
the many-body Lindblad equation exactly in any dimension. As solution we obtain
pure states at any finite value of the dissipation strength and any system
size. They are characterized by a helical stationary magnetization profile and
a superdiffusive ballistic current of order one, independent of system size
even when the quantum spin system is not integrable. These results are derived
in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its
higher-spin generalizations (which include for spin-1 the integrable
Zamolodchikov-Fateev model and the bi-quadratic Heisenberg chain). The
extension of the results to higher dimensions is straightforward.Comment: 23 pages, 2 figure
Asymmetric simple exclusion process on a ring conditioned on enhanced flux
We show that in the asymmetric simple exclusion process (ASEP) on a ring,
conditioned on carrying a large flux, the particle experience an effective
long-range potential which in the limit of very large flux takes the simple
form , where are the particle positions, similar to the effective
potential between the eigenvalues of the circular unitary ensemble in random
matrices. Effective hopping rates and various quasistationary probabilities
under such a conditioning are found analytically using the Bethe ansatz and
determinantal free fermion techniques. Our asymptotic results extend to the
limit of large current and large activity for a family of reaction-diffusion
processes with on-site exclusion between particles. We point out an intriguing
generic relation between classical stationary probability distributions for
conditioned dynamics and quantum ground state wave functions, in particular, in
the case of exclusion processes, for free fermions.Comment: submitted to J. Stat. Mec
Phase-plane analysis of driven multi-lane exclusion models
We show how a fixed point based boundary-layer analysis technique can be used
to obtain the steady-state particle density profiles of driven exclusion
processes on two-lane systems with open boundaries. We have considered two
distinct two-lane systems. In the first, particles hop on the lanes in one
direction obeying exclusion principle and there is no exchange of particles
between the lanes. The hopping on one lane is affected by the particle
occupancies on the other, which thereby introduces an indirect interaction
among the lanes. Through a phase plane analysis of the boundary layer equation,
we show why the bulk density undergoes a sharp change as the interaction
between the lanes is increased. The second system involves one lane with driven
exclusion process and the other with biased diffusion of particles. In contrast
to the previous model, here there is a direct interaction between the lanes due
to particle exchange between them. In this model, we have looked at two
possible scenarios with constant (flat) and non-constant bulk profiles. The
fixed point based boundary layer method provides a new perspective on several
aspects including those related to maximal/minimal current phases,
possibilities of shocks under very restricted boundary conditions for the flat
profile but over a wide range of boundary conditions for the non-constant
profile.Comment: 13 pages, 17 figure
Two-Channel Totally Asymmetric Simple Exclusion Processes
Totally asymmetric simple exclusion processes, consisting of two coupled
parallel lattice chains with particles interacting with hard-core exclusion and
moving along the channels and between them, are considered. In the limit of
strong coupling between the channels, the particle currents, density profiles
and a phase diagram are calculated exactly by mapping the system into an
effective one-channel totally asymmetric exclusion model. For intermediate
couplings, a simple approximate theory, that describes the particle dynamics in
vertical clusters of two corresponding parallel sites exactly and neglects the
correlations between different vertical clusters, is developed. It is found
that, similarly to the case of one-channel totally asymmetric simple exclusion
processes, there are three stationary state phases, although the phase
boundaries and stationary properties strongly depend on inter-channel coupling.
An extensive computer Monte Carlo simulations fully support the theoretical
predictions.Comment: 13 pages, 10 figure
Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
We consider a driven diffusive system with two types of particles, A and B,
coupled at the ends to reservoirs with fixed particle densities. To define
stochastic dynamics that correspond to boundary reservoirs we introduce
projection measures. The stationary state is shown to be approached dynamically
through an infinite reflection of shocks from the boundaries. We argue that
spontaneous symmetry breaking observed in similar systems is due to placing
effective impurities at the boundaries and therefore does not occur in our
system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure
Infinite reflections of shock fronts in driven diffusive systems with two species
Interaction of a domain wall with boundaries of a system is studied for a
class of stochastic driven particle models. Reflection maps are introduced for
the description of this process. We show that, generically, a domain wall
reflects infinitely many times from the boundaries before a stationary state
can be reached. This is in an evident contrast with one-species models where
the stationary density is attained after just one reflection.Comment: 11 pages, 8 eps figs, to appearin JPhysA 01.200
Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
We obtain the exact solution of the one-loop mode-coupling equations for the
dynamical structure function in the framework of non-linear fluctuating
hydrodynamics in one space dimension for the strictly hyperbolic case where all
characteristic velocities are different. All solutions are characterized by
dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers,
which includes the golden mean as a limiting case. The scaling form of all
higher Fibonacci modes are asymmetric L\'evy-distributions. Thus a hierarchy of
new dynamical universality classes is established. We also compute the precise
numerical value of the Pr\"ahofer-Spohn scaling constant to which scaling
functions obtained from mode coupling theory are sensitive.Comment: PACS classification: \pacs{05.60.Cd, 05.20.Jj, 05.70.Ln, 47.10.-g
Fibonacci family of dynamical universality classes
Universality is a well-established central concept of equilibrium physics.
However, in systems far away from equilibrium a deeper understanding of its
underlying principles is still lacking. Up to now, a few classes have been
identified. Besides the diffusive universality class with dynamical exponent
another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ)
class with . It appears e.g. in low-dimensional dynamical phenomena far
from thermal equilibrium which exhibit some conservation law. Here we show that
both classes are only part of an infinite discrete family of non-equilibrium
universality classes. Remarkably their dynamical exponents are given
by ratios of neighbouring Fibonacci numbers, starting with either (if
a KPZ mode exist) or (if a diffusive mode is present). If neither a
diffusive nor a KPZ mode are present, all dynamical modes have the Golden Mean
as dynamical exponent. The universal scaling functions of
these Fibonacci modes are asymmetric L\'evy distributions which are completely
fixed by the macroscopic current-density relation and compressibility matrix of
the system and hence accessible to experimental measurement.Comment: 8 pages, 5 Figs (2 Figure revised, one new Figure added), revised
introductio
Boundary-induced phase transitions in traffic flow
Boundary-induced phase transitions are one of the surprising phenomena
appearing in nonequilibrium systems. These transitions have been found in
driven systems, especially the asymmetric simple exclusion process. However, so
far no direct observations of this phenomenon in real systems exists. Here we
present evidence for the appearance of such a nonequilibrium phase transition
in traffic flow occurring on highways in the vicinity of on- and off-ramps.
Measurements on a German motorway close to Cologne show a first-order
nonequilibrium phase transition between a free-flow phase and a congested
phase. It is induced by the interplay of density waves (caused by an on-ramp)
and a shock wave moving on the motorway. The full phase diagram, including the
effect of off-ramps, is explored using computer simulations and suggests means
to optimize the capacity of a traffic network.Comment: 5 figures, revte
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