1,726 research outputs found
Real-space renormalisation group approach to driven diffusive systems
We introduce a real-space renormalisation group procedure for driven
diffusive systems which predicts both steady state and dynamic properties. We
apply the method to the boundary driven asymmetric simple exclusion process and
recover exact results for the steady state phase diagram, as well as the
crossovers in the relaxation dynamics for each phase.Comment: 10 pages, 5 figure
Quantum Scaling Approach to Nonequilibrium Models
Stochastic nonequilibrium exclusion models are treated using a real space
scaling approach. The method exploits the mapping between nonequilibrium and
quantum systems, and it is developed to accommodate conservation laws and
duality symmetries, yielding exact fixed points for a variety of exclusion
models. In addition, it is shown how the asymmetric simple exclusion process in
one dimension can be written in terms of a classical Hamiltonian in two
dimensions using a Suzuki-Trotter decomposition.Comment: 17 page
Spatially heterogeneous dynamics in granular compaction
We prove the emergence of spatially correlated dynamics in slowly compacting
dense granular media by analyzing analytically and numerically multi-point
correlation functions in a simple particle model characterized by slow
non-equilibrium dynamics. We show that the logarithmically slow dynamics at
large times is accompanied by spatially extended dynamic structures that
resemble the ones observed in glass-forming liquids and dense colloidal
suspensions. This suggests that dynamic heterogeneity is another key common
feature present in very different jamming materials.Comment: 4 pages, 3 figure
Randomly Diluted e_g Orbital-Ordered Systems
Dilution effects on the long-range ordered state of the doubly degenerate
orbital are investigated. Quenched impurities without the orbital degree
of freedom are introduced in the orbital model where the long-range order is
realized by the order-from-disorder mechanism. It is shown by the Monte-Carlo
simulation and the cluster-expansion method that a decrease in the orbital
ordering temperature by dilution is remarkable in comparison with that in the
randomly diluted spin models. Tiltings of orbitals around impurity cause this
unique dilution effects on the orbital systems. The present theory provides a
new view point for the recent experiments in KCuZnF.Comment: 4 pages, 4 figure
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
Duality and phase diagram of one dimensional transport
The observation of duality by Mukherji and Mishra in one dimensional
transport problems has been used to develop a general approach to classify and
characterize the steady state phase diagrams. The phase diagrams are determined
by the zeros of a set of coarse-grained functions without the need of detailed
knowledge of microscopic dynamics. In the process, a new class of
nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files
Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Disordered two-dimensional superconductors: roles of temperature and interaction strength
We have considered the half-filled disordered attractive Hubbard model on a
square lattice, in which the on-site attraction is switched off on a fraction
of sites, while keeping a finite on the remaining ones. Through Quantum
Monte Carlo (QMC) simulations for several values of and , and for system
sizes ranging from to , we have calculated the
configurational averages of the equal-time pair structure factor , and,
for a more restricted set of variables, the helicity modulus, , as
functions of temperature. Two finite-size scaling {\it ansatze} for have
been used, one for zero-temperature and the other for finite temperatures. We
have found that the system sustains superconductivity in the ground state up to
a critical impurity concentration, , which increases with , at least up
to U=4 (in units of the hopping energy). Also, the normalized zero-temperature
gap as a function of shows a maximum near , for . Analyses of the helicity modulus and of the pair structure factor
led to the determination of the critical temperature as a function of , for
4 and 6: they also show maxima near , with the highest
increasing with in this range. We argue that, overall, the observed
behavior results from both the breakdown of CDW-superconductivity degeneracy
and the fact that free sites tend to "push" electrons towards attractive sites,
the latter effect being more drastic at weak couplings.Comment: 9 two-column pages, 14 figures, RevTe
Domain scaling and marginality breaking in the random field Ising model
A scaling description is obtained for the --dimensional random field Ising
model from domains in a bar geometry. Wall roughening removes the marginality
of the case, giving the correlation length in , and for power law behaviour with
, . Here, (lattice, continuum) is one of four rough wall exponents provided by the
theory. The analysis is substantiated by three different numerical techniques
(transfer matrix, Monte Carlo, ground state algorithm). These provide for
strips up to width basic ingredients of the theory, namely free energy,
domain size, and roughening data and exponents.Comment: ReVTeX v3.0, 19 pages plus 19 figures uuencoded in a separate file.
These are self-unpacking via a shell scrip
A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model
This paper introduces a position-space renormalization-group approach for
nonequilibrium systems and applies the method to a driven stochastic
one-dimensional gas with open boundaries. The dynamics are characterized by
three parameters: the probability that a particle will flow into the
chain to the leftmost site, the probability that a particle will flow
out from the rightmost site, and the probability that a particle will jump
to the right if the site to the right is empty. The renormalization-group
procedure is conducted within the space of these transition probabilities,
which are relevant to the system's dynamics. The method yields a critical point
at ,in agreement with the exact values, and the critical
exponent , as compared with the exact value .Comment: 14 pages, 4 figure
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