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