102 research outputs found
Far-from-equilibrium transport with constrained resources
The totally asymmetric simple exclusion process (TASEP) is a well studied
example of far-from-equilibrium dynamics. Here, we consider a TASEP with open
boundaries but impose a global constraint on the total number of particles. In
other words, the boundary reservoirs and the system must share a finite supply
of particles. Using simulations and analytic arguments, we obtain the average
particle density and current of the system, as a function of the boundary rates
and the total number of particles. Our findings are relevant to biological
transport problems if the availability of molecular motors becomes a
rate-limiting factor.Comment: 14 pages, 7 figures, uses iopart12.clo and iopart.cl
Non-equilibrium stationary state of a two-temperature spin chain
A kinetic one-dimensional Ising model is coupled to two heat baths, such that
spins at even (odd) lattice sites experience a temperature ().
Spin flips occur with Glauber-type rates generalised to the case of two
temperatures. Driven by the temperature differential, the spin chain settles
into a non-equilibrium steady state which corresponds to the stationary
solution of a master equation. We construct a perturbation expansion of this
master equation in terms of the temperature difference and compute explicitly
the first two corrections to the equilibrium Boltzmann distribution. The key
result is the emergence of additional spin operators in the steady state,
increasing in spatial range and order of spin products. We comment on the
violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte
Phase diagram of two-lane driven diffusive systems
We consider a large class of two-lane driven diffusive systems in contact
with reservoirs at their boundaries and develop a stability analysis as a
method to derive the phase diagrams of such systems. We illustrate the method
by deriving phase diagrams for the asymmetric exclusion process coupled to
various second lanes: a diffusive lane; an asymmetric exclusion process with
advection in the same direction as the first lane, and an asymmetric exclusion
process with advection in the opposite direction. The competing currents on the
two lanes naturally lead to a very rich phenomenology and we find a variety of
phase diagrams. It is shown that the stability analysis is equivalent to an
`extremal current principle' for the total current in the two lanes. We also
point to classes of models where both the stability analysis and the extremal
current principle fail
Frozen Disorder in a Driven System
We investigate the effects of quenched disorder on the universal properties
of a randomly driven Ising lattice gas. The Hamiltonian fixed point of the pure
system becomes unstable in the presence of a quenched local bias, giving rise
to a new fixed point which controls a novel universality class. We determine
the associated scaling forms of correlation and response functions, quoting
critical exponents to two-loop order in an expansion around the upper critical
dimension d.Comment: 5 pages RevTex. Uses multicol.sty. Accepted for publication in PR
Freezing by Heating in a Driven Mesoscopic System
We investigate a simple model corresponding to particles driven in opposite
directions and interacting via a repulsive potential. The particles move
off-lattice on a periodic strip and are subject to random forces as well. We
show that this model - which can be considered as a continuum version of some
driven diffusive systems - exhibits a paradoxial, new kind of transition called
here ``freezing by heating''. One interesting feature of this transition is
that a crystallized state with a higher total energy is obtained from a fluid
state by increasing the amount of fluctuations.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.html and
http://angel.elte.hu/~vicsek
Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model
A two species particle model on an open chain with dynamics which is
non-conserving in the bulk is introduced. The dynamical rules which define the
model obey a symmetry between the two species. The model exhibits a rich
behavior which includes spontaneous symmetry breaking and localized shocks. The
phase diagram in several regions of parameter space is calculated within
mean-field approximation, and compared with Monte-Carlo simulations. In the
limit where fluctuations in the number of particles in the system are taken to
zero, an exact solution is obtained. We present and analyze a physical picture
which serves to explain the different phases of the model
Energy flux distribution in a two-temperature Ising model
The nonequilibrium steady state of an infinite-range Ising model is studied.
The steady state is obtained by dividing the spins into two groups and
attaching them to two heat baths generating spin flips at different
temperatures. In the thermodynamic limit, the resulting dynamics can be solved
exactly, and the probability flow in the phase space can be visualized. We can
calculate the steady state fluctuations far from equilibrium and, in
particular, we find the exact probability distribution of the energy current in
both the high- and low-temperature phase.Comment: 19 pages, 4 figure
Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
When Lenz proposed a simple model for phase transitions in magnetism, he
couldn't have imagined that the "Ising model" was to become a jewel in field of
equilibrium statistical mechanics. Its role spans the spectrum, from a good
pedagogical example to a universality class in critical phenomena. A quarter
century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing
a seemingly trivial modification to the Ising lattice gas, they took it into
the vast realms of non-equilibrium statistical mechanics. An abundant variety
of unexpected behavior emerged and caught many of us by surprise. We present a
brief review of some of the new insights garnered and some of the outstanding
puzzles, as well as speculate on the model's role in the future of
non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting,
Rutgers, NJ (December, 2008
Traffic jams induced by rare switching events in two-lane transport
We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular traffic. Introducing a coupling between the internal states by allowing particles to switch from one to another induces an intriguing polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for the density profiles is discovered, with localized domain walls in the density profile of one of the internal states being feasible. We derive the shape of the density profiles as well as resulting phase diagrams analytically by a mean-field approximation and a continuum limit. Continuous as well as discontinuous lines of phase transition emerge, their intersections induce multi-critical behaviour
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
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