500 research outputs found
Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory
Through a Euclidean path integral we establish that the density fluctuations
of a Fermi fluid in one dimension are related to vicinal surfaces and to the
stochastic dynamics of particles interacting through long range forces with
inverse distance decay. In the surface picture one easily obtains the Haldane
relation and identifies the scaling exponents governing the low energy,
Luttinger liquid behavior. For the stochastic particle model we develop a
hydrodynamic fluctuation theory, through which in some cases the large distance
Gaussian fluctuations are proved nonperturbatively
Transfer matrices for the totally asymmetric exclusion process
We consider the totally asymmetric simple exclusion process (TASEP) on a
finite lattice with open boundaries. We show, using the recursive structure of
the Markov matrix that encodes the dynamics, that there exist two transfer
matrices and that intertwine the Markov
matrices of consecutive system sizes:
. This semi-conjugation property of
the dynamics provides an algebraic counterpart for the matrix-product
representation of the steady state of the process.Comment: 7 page
Kinetics of A+B--->0 with Driven Diffusive Motion
We study the kinetics of two-species annihilation, A+B--->0, when all
particles undergo strictly biased motion in the same direction and with an
excluded volume repulsion between same species particles. It was recently shown
that the density in this system decays as t^{-1/3}, compared to t^{-1/4}
density decay in A+B--->0 with isotropic diffusion and either with or without
the hard-core repulsion. We suggest a relatively simple explanation for this
t^{-1/3} decay based on the Burgers equation. Related properties associated
with the asymptotic distribution of reactants can also be accounted for within
this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on
request from S
Some Exact Results for the Exclusion Process
The asymmetric simple exclusion process (ASEP) is a paradigm for
non-equilibrium physics that appears as a building block to model various
low-dimensional transport phenomena, ranging from intracellular traffic to
quantum dots. We review some recent results obtained for the system on a
periodic ring by using the Bethe Ansatz. We show that this method allows to
derive analytically many properties of the dynamics of the model such as the
spectral gap and the generating function of the current. We also discuss the
solution of a generalized exclusion process with -species of particles and
explain how a geometric construction inspired from queuing theory sheds light
on the Matrix Product Representation technique that has been very fruitful to
derive exact results for the ASEP.Comment: 21 pages; Proceedings of STATPHYS24 (Cairns, Australia, July 2010
Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
The one-dimensional partially asymmetric simple exclusion process with open
boundaries is considered. The stationary state, which is known to be
constructed in a matrix product form, is studied by applying the theory of
q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the
average density profile is computed in the thermodynamic limit. The phase
diagram for the correlation length, which was conjectured in the previous
work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure
A new class of integrable diffusion-reaction processes
We consider a process in which there are two types of particles, A and B, on
an infinite one-dimensional lattice. The particles hop to their adjacent sites,
like the totally asymmetric exclusion process (ASEP), and have also the
following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate.
We study this process by imposing four boundary conditions on ASEP master
equation. It is shown that this model is integrable, in the sense that its
N-particle S-matrix is factorized into a product of two-particle S-matrices
and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter
equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the
two-particle conditional probabilities are found exactly.
Further, by imposing four reasonable physical conditions on two-species
diffusion-reaction processes (where the most important ones are the equality of
the reaction rates and the conservation of the number of particles in each
reaction), we show that among the 4096 types of the interactions which have
these properties and can be modeled by a master equation and an appropriate set
of boundary conditions, there are only 28 independent interactions which are
integrable. We find all these interactions and also their corresponding wave
functions. Some of these may be new solutions of quantum Yang-Baxter equation.Comment: LaTex,16 pages, some typos are corrected, will be appeared in Phys.
Rev. E (2000
Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
For the symmetric simple exclusion process on an infinite line, we calculate
exactly the fluctuations of the integrated current during time
through the origin when, in the initial condition, the sites are occupied with
density on the negative axis and with density on the positive
axis. All the cumulants of grow like . In the range where , the decay of the distribution of is
non-Gaussian. Our results are obtained using the Bethe ansatz and several
identities recently derived by Tracy and Widom for exclusion processes on the
infinite line.Comment: 2 figure
Hidden symmetries in the asymmetric exclusion process
We present a spectral study of the evolution matrix of the totally asymmetric
exclusion process on a ring at half filling. The natural symmetries
(translation, charge conjugation combined with reflection) predict only two
fold degeneracies. However, we have found that degeneracies of higher order
also exist and, as the system size increases, higher and higher orders appear.
These degeneracies become generic in the limit of very large systems. This
behaviour can be explained by the Bethe Ansatz and suggests the presence of
hidden symmetries in the model.
Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe
Ansatz.Comment: 16 page
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
Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite
dimensional Hilbert space and generated by unbounded Hamiltonians. In
particular, we consider quantum harmonic and certain anharmonic lattice
systems
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