3,086 research outputs found
Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
We study the one dimensional partially asymmetric simple exclusion process
(ASEP) with open boundaries, that describes a system of hard-core particles
hopping stochastically on a chain coupled to reservoirs at both ends. Derrida,
Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the
stationary probability distribution of this model can be represented as a trace
on a quadratic algebra, closely related to the deformed oscillator-algebra. We
construct all finite dimensional irreducible representations of this algebra.
This enables us to compute the stationary bulk density as well as all
correlation lengths for the ASEP on a set of special curves of the phase
diagram.Comment: 18 pages, Latex, 1 EPS figur
Persistence in the zero-temperature dynamics of the -states Potts model on undirected-directed Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs
The zero-temperature Glauber dynamics is used to investigate the persistence
probability in the Potts model with , ,..., states on {\it directed} and {\it
undirected} Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs. In
this model it is found that decays exponentially to zero in short times
for {\it directed} and {\it undirected} Erd\"os-R\'enyi random graphs. For {\it
directed} and {\it undirected} Barab\'asi-Albert networks, in contrast it
decays exponentially to a constant value for long times, i.e, is
different from zero for all values (here studied) from ; this shows "blocking" for all these values. Except that for
in the {\it undirected} case tends exponentially to zero;
this could be just a finite-size effect since in the other "blocking" cases you
may have only a few unchanged spins.Comment: 14 pages, 8 figures for IJM
The political import of deconstruction—Derrida’s limits?: a forum on Jacques Derrida’s specters of Marx after 25 Years, part I
Jacques Derrida delivered the basis of The Specters of Marx: The State of the Debt, the Work of Mourning, & the New International as a plenary address at the conference ‘Whither Marxism?’ hosted by the University of California, Riverside, in 1993. The longer book version was published in French the same year and appeared in English and Portuguese the following year. In the decade after the publication of Specters, Derrida’s analyses provoked a large critical literature and invited both consternation and celebration by figures such as Antonio Negri, Wendy Brown and Frederic Jameson. This forum seeks to stimulate new reflections on Derrida, deconstruction and Specters of Marx by considering how the futures past announced by the book have fared after an eventful quarter century. Maja Zehfuss, Antonio Vázquez-Arroyo and Dan Bulley and Bal Sokhi-Bulley offer sharp, occasionally exasperated, meditations on the political import of deconstruction and the limits of Derrida’s diagnoses in Specters of Marx but also identify possible paths forward for a global politics taking inspiration in Derrida’s work of the 1990s
One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle
The effect of a moving defect particle for the one-dimensional partially
asymmetric simple exclusion process on a ring is considered. The current of the
ordinary particles, the speed of the defect particle and the density profile of
the ordinary particles are calculated exactly. The phase diagram for the
correlation length is identified. As a byproduct, the average and the variance
of the particle density of the one-dimensional partially asymmetric simple
exclusion process with open boundaries are also computed.Comment: 23 pages, 1 figur
Exact solution of a Levy walk model for anomalous heat transport
The Levy walk model is studied in the context of the anomalous heat
conduction of one dimensional systems. In this model the heat carriers execute
Levy-walks instead of normal diffusion as expected in systems where Fourier's
law holds. Here we calculate exactly the average heat current, the large
deviation function of its fluctuations and the temperature profile of the
Levy-walk model maintained in a steady state by contact with two heat baths
(the open geometry). We find that the current is non-locally connected to the
temperature gradient. As observed in recent simulations of mechanical models,
all the cumulants of the current fluctuations have the same system-size
dependence in the open geometry. For the ring geometry, we argue that a size
dependent cut-off time is necessary for the Levy walk model to behave as
mechanical models. This modification does not affect the results on transport
in the open geometry for large enough system sizes.Comment: 5 pages, 2 figure
Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase
We consider the low-temperature disorder-dominated phase of the
directed polymer in a random potentiel in dimension 1+1 (where )
and 1+3 (where ). To characterize the localization properties of
the polymer of length , we analyse the statistics of the weights of the last monomer as follows. We numerically compute the probability
distributions of the maximal weight , the probability distribution of the parameter as well as the average values of the higher order
moments . We find that there exists a
temperature such that (i) for , the distributions
and present the characteristic Derrida-Flyvbjerg
singularities at and for . In particular, there
exists a temperature-dependent exponent that governs the main
singularities and as well as the power-law decay of the moments . The exponent grows from the value
up to . (ii) for , the
distribution vanishes at some value , and accordingly the
moments decay exponentially as in . The
histograms of spatial correlations also display Derrida-Flyvbjerg singularities
for . Both below and above , the study of typical and
averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure
Exact solution of an exclusion process with three classes of particles and vacancies
We present an exact solution for an asymmetric exclusion process on a ring
with three classes of particles and vacancies. Using a matrix product Ansatz,
we find explicit expressions for the weights of the configurations in the
stationary state. The solution involves tensor products of quadratic algebras.Comment: 18 pages, no figures, LaTe
Exact Shock Profile for the ASEP with Sublattice-Parallel Update
We analytically study the one-dimensional Asymmetric Simple Exclusion Process
(ASEP) with open boundaries under sublattice-parallel updating scheme. We
investigate the stationary state properties of this model conditioned on
finding a given particle number in the system. Recent numerical investigations
have shown that the model possesses three different phases in this case. Using
a matrix product method we calculate both exact canonical partition function
and also density profiles of the particles in each phase. Application of the
Yang-Lee theory reveals that the model undergoes two second-order phase
transitions at critical points. These results confirm the correctness of our
previous numerical studies.Comment: 12 pages, 3 figures, accepted for publication in Journal of Physics
Symmetry breaking through a sequence of transitions in a driven diffusive system
In this work we study a two species driven diffusive system with open
boundaries that exhibits spontaneous symmetry breaking in one dimension. In a
symmetry broken state the currents of the two species are not equal, although
the dynamics is symmetric. A mean field theory predicts a sequence of two
transitions from a strongly symmetry broken state through an intermediate
symmetry broken state to a symmetric state. However, a recent numerical study
has questioned the existence of the intermediate state and instead suggested a
single discontinuous transition. In this work we present an extensive numerical
study that supports the existence of the intermediate phase but shows that this
phase and the transition to the symmetric phase are qualitatively different
from the mean-field predictions.Comment: 19 pages, 12 figure
Scaling behavior of a one-dimensional correlated disordered electronic System
A one-dimensional diagonal tight binding electronic system with correlated
disorder is investigated. The correlation of the random potential is
exponentially decaying with distance and its correlation length diverges as the
concentration of "wrong sign" approaches to 1 or 0. The correlated random
number sequence can be generated easily with a binary sequence similar to that
of a one-dimensional spin glass system. The localization length (LL) and the
integrated density of states (IDOS) for long chains are computed. A comparison
with numerical results is made with the recently developed scaling technique
results. The Coherent Potential Approximation (CPA) is also adopted to obtain
scaling functions for both the LL and the IDOS. We confirmed that the scaling
functions show a crossover near the band edge and establish their relation to
the concentration. For concentrations near to 0 or 1 (longer correlation length
case), the scaling behavior is followed only for a very limited range of the
potential strengths.Comment: will appear in PR
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