9,365 research outputs found
An exactly solvable lattice model for inhomogeneous interface growth
We study the dynamics of an exactly solvable lattice model for inhomogeneous
interface growth. The interface grows deterministically with constant velocity
except along a defect line where the growth process is random. We obtain exact
expressions for the average height and height fluctuations as functions of
space and time for an initially flat interface. For a given defect strength
there is a critical angle between the defect line and the growth direction
above which a cusp in the interface develops. In the mapping to polymers in
random media this is an example for the transverse Meissner effect.
Fluctuations around the mean shape of the interface are Gaussian.Comment: 10 pages, late
Dynamic Matrix Ansatz for Integrable Reaction-Diffusion Processes
We show that the stochastic dynamics of a large class of one-dimensional
interacting particle systems may be presented by integrable quantum spin
Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an
alternative description of these processes in terms of a time-dependent
operator algebra with quadratic relations. These relations generate the Bethe
ansatz equations for the spectrum and turn the calculation of time-dependent
expectation values into the problem of either finding representations of this
algebra or of solving functional equations for the initial values of the
operators. We use both strategies for the study of two specific models: (i) We
construct a two-dimensional time-dependent representation of the algebra for
the symmetric exclusion process with open boundary conditions. In this way we
obtain new results on the dynamics of this system and on the eigenvectors and
eigenvalues of the corresponding quantum spin chain, which is the isotropic
Heisenberg ferromagnet with non-diagonal, symmetry-breaking boundary fields.
(ii) We consider the non-equilibrium spin relaxation of Ising spins with
zero-temperature Glauber dynamics and an additional coupling to an
infinite-temperature heat bath with Kawasaki dynamics. We solve the functional
equations arising from the algebraic description and show non-perturbatively on
the level of all finite-order correlation functions that the coupling to the
infinite-temperature heat bath does not change the late-time behaviour of the
zero-temperature process. The associated quantum chain is a non-hermitian
anisotropic Heisenberg chain related to the seven-vertex model.Comment: Latex, 23 pages, to appear in European Physical Journal
Importance of boundary effects in diffusion of hydrocarbon molecules in a one-dimensional zeolite channel
Single-file diffusion of propane and toluene molecules inside a narrow,
effectively one-dimensional zeolite pore was experimentally studied by
Czaplewski {\sl et al.} Using a stochastic lattice gas approach, we obtain an
analytical description of this process for the case of single-component
loading. We show that a good quantitative agreement with the experimental data
for the desorption temperature of the hydrocarbon molecules can be obtained if
the desorption process from the boundary is associated with a higher activation
energy than the diffusion process in the bulk. We also present Dynamical Monte
Carlo simulation results for two-component loading which demonstrate in
agreement with the experimental findings the effects of mutual blockage of the
molecules due to single-file diffusion.Comment: Revised and final versio
Diffusion of a hydrocarbon mixture in a one-dimensional zeolite channel: an exclusion model approach
Zeolite channels can be used as effective hydrocarbon traps. Earlier
experiments (Czaplewski {\sl et al.}, 2002) show that the presence of large
aromatic molecules (toluene) block the diffusion of light hydrocarbon molecules
(propane) inside the narrow pore of a zeolite sample. As a result, the
desorption temperature of propane is significantly higher in the binary mixture
than in the single component case. In order to obtain further insight into
these results, we use a simple lattice gas model of diffusion of hard-core
particles to describe the diffusive transport of two species of molecules in a
one-dimensional zeolite channel. Our dynamical Monte Carlo simulations show
that taking into account an Arrhenius dependence of the single molecule
diffusion coefficient on temperature, one can explain many significant features
of the temperature programmed desorption profile observed in experiments.
However, on a closer comparison of the experimental curve and our simulation
data, we find that it is not possible to reproduce the higher propane current
than toluene current near the desorption peak seen in experiment. We argue that
this is caused by a violation of strict single-file behavior.Comment: Accepted for publication in the special issue "Diffusion in
Micropores" of the journal Microporous and Mesoporous Material
Nonequilibrium field-induced phase separation in single-file diffusion
Using an analytically tractable lattice model for reaction-diffusion
processes of hard-core particles we demonstrate that under nonequilibrium
conditions phase coexistence may arise even if the system is effectively
one-dimensional as e.g. in the channel system of some zeolites or in artificial
optical lattices. In our model involving two species of particles a
steady-state particle current is maintained by a density gradient between the
channel boundaries and by the influence of an external driving force. This
leads to the development of a fluctuating but always microscopically sharp
interface between two domains of different densities which are fixed by the
boundary chemical potentials. The internal structure of the interface becomes
very simple for strong driving force. We calculate the drift velocity and
diffusion coefficient of the interface in terms of the microscopic model
parameters.Comment: 38 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
Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
We study the asymmetric zero-range process (ZRP) with L sites and open
boundaries, conditioned to carry an atypical current. Using a generalized Doob
h-transform we compute explicitly the transition rates of an effective process
for which the conditioned dynamics are typical. This effective process is a
zero-range process with renormalized hopping rates, which are space dependent
even when the original rates are constant. This leads to non-trivial density
profiles in the steady state of the conditioned dynamics, and, under generic
conditions on the jump rates of the unconditioned ZRP, to an intriguing
supercritical bulk region where condensates can grow. These results provide a
microscopic perspective on macroscopic fluctuation theory (MFT) for the weakly
asymmetric case: It turns out that the predictions of MFT remain valid in the
non-rigorous limit of finite asymmetry. In addition, the microscopic results
yield the correct scaling factor for the asymmetry that MFT cannot predict.Comment: 26 pages, 4 figure
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