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Equilibrium statistical mechanics studies random fields distrib- uted according to a Gibbs probability measure. Such random fields can be equipped with a stochastic dynamics given by a Markov process with the correspondingly high-dimensional state space. One particular case are sto- chastic partial differential equations suitably regularized. Another common version is to consider the evolution of random fields taking only values 0 or 1. The workshop was concerned with an understanding of qualitative properties of such high-dimensional Markov processes. Of particular interest are non- reversible dynamics for which the stationary measures are determined only through the dynamics and not given a priori (as would be the case for re- versible dynamics). As a general observation, properties on a large scale do not depend on the precise details of the local updating rules. Such kind of universality was a guiding theme of our workshop.

This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy$_1$ process., Comment: Published at http://dx.doi.org/10.1214/14-AAP1025 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

International audience; We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved fields. Through numerical simulations the peak structure of the steady state space-time correlations is determined and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the completely asymmetric Levy distribution with parameter $\alpha=5/3$. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.

We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution we consider initial configurations distributed according to a Poisson point process with constant intensity, which makes the process space-time stationary. We prove convergence to the Airy process for stationary the case. As a byproduct we obtain a novel representation of the finite-dimensional distributions of this process. Our method differs from the one used for the TASEP and the KPZ equation by removing the initial step only after the limit $t\to\infty$. This leads to a new universal cross-over process., Comment: 55 pages, 10 figures

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE in a hydrodynamic form of a continuity and an Euler equation. Respecting conservation laws, dissipation and noise due to the system's chaos are added, thus giving us a nonlinear stochastic field theory in general and the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by investigating the non-zero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (a.k.a. nonlinear Schrodinger equation), ranging from nonlinear optics to cold gases, we expect this remarkable mapping to the KPZ equation to be of paramount importance and far reaching consequences., Comment: 6 pages, 2 figures

We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives at Brownian motions with oblique reflections. For this model we prove a Bethe ansatz formula for the transition probability and self-duality. In case of half-Poisson initial data, duality is used to arrive at a Fredholm determinant for the generating function of the number of particles to the left of some reference point at any positive time. A formal asymptotics for this determinant establishes the link to the Kardar-Parisi-Zhang universality class., Comment: 34 pages, 2 figures

While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters the profile develops a rarefaction wave, while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain we will demonstrate that the time-integrated current has a deterministic contribution, linear in time $t$, and fluctuations of size $t^{1/3}$ with a Tracy-Widom distributed random amplitude., Comment: 5 figures

For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, $f$, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of this limit on the basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic time span, the argument can be made mathematically precise following the seminal work of Lanford. In this article a corresponding programme is undertaken for weakly nonlinear, both discrete and continuum, wave equations. Our working example is the harmonic lattice with a weakly nonquadratic on-site potential. We argue that the role of the Boltzmann $f$-function is taken over by the Wigner function, which is a very convenient device to filter the slow degrees of freedom. The Wigner function, so to speak, labels locally the covariances of dynamically almost stationary measures. One route to the phonon Boltzmann equation is a Gaussian decoupling, which is based on the fact that the purely harmonic dynamics has very good mixing properties. As a further approach the expansion in terms of Feynman diagrams is outlined. Both methods are extended to the quantized version of the weakly nonlinear wave equation. The resulting phonon Boltzmann equation has been hardly studied on a rigorous level. As one novel contribution we establish that the spatially homogeneous stationary solutions are precisely the thermal Wigner functions. For three phonon processes such a result requires extra conditions on the dispersion law. We also outline the reasoning leading to Fourier's law for heat conduction., Comment: special issue on "Kinetic Theory", Journal of Statistical Physics, improved version

For suitably discretized versions of the Kardar—Parisi—Zhang equation in one space dimension, exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of mass $m$ and charge $e$. This system forms a bound state with binding energy $E_{\rm bin} = me^4Z^2/2$ to leading order in $e$. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that $ E_{\rm bin} = me^4 Z^2/2 + c_0 e^6 + \Ow(e^7 \ln e)$ with explicit coefficient $c_0$ and independent of the ultraviolet cutoff. $c_0$ can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum., 30 pages, AMSLatex

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann-Hilbert problem related to the Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore [1] obtained from the mode coupling approximation., 24 pages, 6 figures, replaced with revised version

We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\phi(\epsi x)$, and vector potential $A(\epsi x)$, with $x \in \R^d$ and $\epsi \ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics., Comment: 37 pages

We establish soliton-like asymptotics for finite energy solutions to classical particle coupled to a scalar wave field. Any solution that goes to infinity as $t\to\infty$ converges to a sum of traveling wave and of outgoing free wave. The convergence holds in global energy norm. The proof uses a non-autonomous integral inequality method.

A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty. Allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds. If V denotes the number of atoms removed, then the grand canonical Boltzmann weight is q V , 0

We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged spin auto-correlation function has an exponential decay in time. We prove that, if the couplings are unbounded, the decay switches to either a power law or a stretched exponential, in general.

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not unitarily equivalent with the Hamiltonian obtained from Euclidean quantization. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Fock space and the two Hamiltonians are unitarily equivalent. We also show that the Euclidean Hamiltonian has no spectral gap.

We prove that in the Euclidean representation of the three-dimensional massless Nelson model, the t = 0 projection of the interacting measure is absolutely continuous with respect to a Gaussian measure with a suitably adjusted mean. We also determine the Hamiltonian in the Fock space over this Gaussian measure space.

We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are negligible and the dressed electron is governed by an effective one-particle Hamiltonian. In the proof only a few generic properties of the full Pauli–Fierz Hamiltonian H PF enter. Most importantly, H PF must have an isolated ground state band for |p| c ≤∞ with p the total momentum and p c indicating that the ground state band may terminate. This structure demands a local approximation theorem, in the sense that the one-particle approximation holds until the semiclassical dynamics violates |p| c . Within this framework we prove an abstract Hilbert space theorem which uses no additional information on the Hamiltonian away from the band of interest. Our result is applicable to other time-dependent semiclassical problems. We discuss semiclassical distributions for the effective one-particle dynamics and show how they can be translated to the full dynamics by our results.

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y−2. Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation.

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Levy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations., Comment: 11 pages, 10 figures

We study the Boltzmann transport equation for the Bose-Hubbard chain in the kinetic regime. The time-dependent Wigner function is matrix-valued with odd dimension due to integer spin. For nearest neighbor hopping only, there are infinitely many additional conservation laws and nonthermal stationary states. Adding longer range hopping amplitudes entails exclusively thermal equilibrium states. We provide a derivation of the Boltzmann equation based on the Hubbard hamiltonian, including general interactions beyond on-site, and illustrate the results by numerical simulations. In particular, convergence to thermal equilibrium states with negative temperature is investigated., 16 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1306.0934

As recently proposed, the long-time behavior of equilibrium time-correlation functions for one-dimensional systems are expected to be captured by a nonlinear extension of fluctuating hydrodynamics. We outline the predictions from the theory aimed at the comparison with molecular dynamics. We report on numerical simulations of a fluid with a hard-shoulder potential and of a hard-point gas with alternating masses. These models have in common that the collision time is zero and their dynamics amounts to iterating collision by collision. The theory is well confirmed, with the twist that the non-universal coefficients are still changing at longest accessible times., 5 figures

We study the total current correlations for anharmonic chains in thermal equilibrium, putting forward predictions based on the second moment sum rule and on nonlinear fluctuating hydrodynamics. We compare with molecular dynamics simulations for hard collision models. For the first time we investigate the full statistics of time-integrated currents. Generically such a quantity has Gaussian statistics on a scale $\sqrt{t}$. But if the time integration has its endpoint at a moving sound peak, then the fluctuations are suppressed and only of order $t^{1/3}$. The statistics is governed by the Baik-Rains distribution, known already from the fluctuating Burgers equation., Comment: 27 pages, 8 figures

We consider an electron coupled to the quantized radiation field in the dipole approximation. Even if the Hamiltonian has no ground state at zero coupling, $ \alpha = 0 $ , the interaction with the quantized radiation field may induce binding. Under suitable assumptions on the external potential, we prove that there exists a critical constant $ \alpha_* \geq 0 $ such that the Hamiltonian has a unique ground state for arbitrary $ \mid\alpha\mid > \alpha_* $ . Moreover an explicit lower bound $ \alpha_c $ of $ \alpha_* $ ¶ is given.

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection., Comment: Revised version. 19 pages, 2 figures

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We investigate higher order corrections with an explicit control on the error terms. The Darwin correction, order (v/c)^2, has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order (v/c)^3 relative to the Coulomb dynamics. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.

We consider the dynamics generated by the Schroedinger operator $H=-{1/2}\Delta + V(x) + W(\epsi x)$, where $V$ is a lattice periodic potential and $W$ an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit $\epsi \to 0$ the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics.

We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian $H$. There is no external potential and $H$ fibers according to the total momentum $p$. We prove that the ground state subspace of $H$ with a total momentum $p$ is two-fold degenerate provided the charge $e$ and the total momentum $p$ are sufficiently small. We also establish that the total angular momentum of the ground state subspace is $\pm1/2$ and study the case of a confining external potential.

We consider the Abraham model of a rigid charge distribution coupled to the electromagnetic field and subject to, on the scale of the charge diameter, slowly varying external potentials. We prove that in the adiabatic limit the motion of the charged particle is governed by a effective Hamiltonian. To next order one has to add as a small correction the relativistically covariant radiation reaction. This third order equation has a repulsive center manifold and the true solution is well approximated by a trajectory on the center manifold.We also prove that in the adiabatic limit the fields are derived from the Lienard-Wiechert potentials of a moving point charge and that the radiated energy is given by Larmor's formula.

We develop a scaling theory for KPZ growth in one dimension by a detailed study of the polynuclear growth (PNG) model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential., Comment: 4 pages, 3 figures, 1 table, RevTeX, revised version, accepted for publication in PRL

We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie on the critical surface. The critical surface is repelling, i.e. any slight deviation from it is amplified and as a result the solution runs away to infinity. On the other hand, Dirac's asymptotic condition (acceleration vanishes for long times) forces the solution to be on the critical manifold. The critical surface can be determined perturbatively. Thereby one obtains an effective second order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap.

(2000). Long—time asymptotics for the coupled maxwell—lorentz equations. Communications in Partial Differential Equations: Vol. 25, No. 3-4, pp. 559-584.

We study the effective dynamics of a mechanical particle coupled to a wave field and subject to the slowly varying potential $V(\varepsilon q)$ with $\varepsilon$ small. To lowest order in $\varepsilon$ the motion of the particle is governed by an effective Hamiltonian. In the next order one obtains "dissipative" terms which describe the radiation reaction. We establish that this dissipative dynamics has a center manifold which is repulsive in the normal direction and which is global, in the sense that for given data and sufficiently small $\varepsilon$ the solution stays on the center manifold forever. We prove that the solutionof the full system is well approximated by the effective dissipative dynamics on its center manifold.

We develop a Laplacian model of interface growth which includes basic features of the anodisation of silicon in hydrofluoric acid. Our aim is to find mechanisms for the characteristic properties of porous silicon formation, such as the transition from electropolishing to pore formation and the typical pore distance. The local etching rate of the interface between the semiconductor and the electrolyte is determined by the local current density. We model the diffusive transport of charge carriers in the semiconductor and of reactants in the electrolyte including the basic features of the electrochemical reaction at the interface. A linear stability analysis of a flat and planar interface is performed in order to study the initial state of pore formation.

We consider a particle coupled to a scalar wave field and subject to the slowly varying potential V ("q) with small ". We prove that if the initial state is close, order " 2 , to a soliton (=dressed particle), then the solution stays forever close to the soliton manifold. This estimate implies that over a time span of order" 1 the radiation losses are negligible and that the motion of the particle is governed by the effective Hamiltonian Heff (q;P )= E(P )+ V ("q) with energy-momentum relationE(P ).

Using Griffiths and Lieb-Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction provided that N=1,2,3,4 and T > T_c.

We extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes describing the evolution of stochastic lattice gases driven in the bulk or through particle reservoirs, general diffusive processes in physical and/or velocity space, as well as Hamiltonian systems with stochastic boundary conditions. For dynamics satisfying local detailed balance we establish a link between the action functional of the fluctuation theorem and the entropy production. This gives, in the linear regime, an alternative derivation of the Green-Kubo formula and the Onsager reciprocity relations. In the nonlinear regime consequences of the new symmetry are harder to come by and the large derivation functional difficult to compute. For the asymmetric simple exclusion process the latter is determined explicitly using the Bethe ansatz in the limit of large N.

We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set S of stationary states in the long time limit t → ±∞. This implies the convergence to some stationary states S ± as t → ±∞ if the set S is discrete. The rate of relaxation to a stable stationary state is determined by spatial decay of initial data. The investigation is inspired by N.Bohr's postulate on transitions to stationary states in quantum systems.

We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a scalar massless Bose field. For an external potential growing at infinity, the ground state exists under fairly general conditions while, for a decaying potential, an unphysical condition on the coupling strength is still needed.

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions., Comment: 9 pages, REVTEX, epsf, 3 postscript figures, submitted to J. Stat. Phys, a wrong character is corrected in eqs. (31) and (32)

We consider an electron bound by some anharmonic external potential and coupled to the quantized radiation field in the dipole approximation. We prove asymptotic completeness for the photon scattering. This means that an arbitrary initial state has a long time asymptotic, which consists of electron plus radiation field in their coupled ground state and finitely many outgoing photons.

We consider the scalar field φ t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ t -field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the -field.

We consider the Harniltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t f oo. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data. 'Supported partly by French-Russian A.M.Liapunov Center of Moscow State University, by research grants of RFBR (9601-00527) and of Volkswagen-Stiftung.

The standard Fermi-Hubbard chain becomes non-integrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small n.n.n. hopping amplitudes one has a rapid relaxation towards the manifold of quasi-stationary states and slow relaxation to the final equilibrium state., 9 figures

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients., 32 pages, 4 figures; Minor correction in the formula for the density