In one and two dimensions,every stationary measure for a stochastic Ising Model is a Gibbs state

It is shown that one and two dimensional (generalized) stochastic Ising models with finite range potentials have only Gibbs states as their stationary measures. This is true even if the stationary measure or the potential is not translation invariant. This extends previously known results which are restricted to translation invariant stationary measures and potentials. In particular if the potential has only one Gibbs state the stochastic Ising Model must be ergodic.Research supported in part by N.S.F. Grant MPS 74-18926Alfred P. Sloan Fellow     

Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

In this paper we describe invariant geometrical structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable. Received: 30 January 1997 / Accepted: 6 April 1997     

Free energy in spin-flip processes is non-increasing

In this paper, we propose a new and shorter proof of the following fact: in a spin-flip process on {–1, +1} ^S , whereS is a countable set, the free energy is non-increasing.Free energy is a well defined functional only for invariant measures under a convenient group of bijections ofS. We formalize this with the notion ofB-ameanability ofS. This frame contains the usual example ofZ ^d under translations but also many nice lattices that are not groups under groups of isometries.For invariant measures, except Gibbs ones, the free energy is strictly decreasing. Among invariant measures, the only stationary measures for the spin-flip process are therefore Gibbs measures. From this result we also deduce an ergodic theorem.The first result on this subject was obtained by Holley [1] for a finite range potential on and some extension by Higuchi, Shiga [2].     

Correlation Spectrum of Quenched and Annealed Equilibrium States for Random Expanding Maps

We show that the integrated transfer operators for positively weighted independent identically distributed smooth expanding systems give rise to annealed equilibrium states for a new variational principle. The unique annealed equilibrium state coincides with the unique annealed Gibbs state. Using work of Ruelle [1990] and Fried [1995] on generalised Fredholm determinants for transfer operators, we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures (yielding exponential decay of correlations), and with the poles of an annealed zeta function, defined also for complex weights. A modified integrated transfer operator is introduced, which describes the (relativised) quenched states studied e.g. by Kifer [1992], and conditions (including SRB) ensuring coincidence of quenched and annealed states are given. For small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of Young and the author [1993]. Received: 16 April 1996 / Accepted: 25 October 1996     

The Gauge-Invariant Spectrum of Local Super-Symmetry as the Universe that is Observed

It is demonstrated that gauge invariant states within local super-symmetry are equivalent to quantized states of global super-symmetry that are preserved by (oblivious to) super-gravitational interactions (analogous to the stationary atomic states that derive from gauge invariance in the theory of Weyl). The cosmology which emerges from this equivalence is unique and finite, and parallels observation. Specifically, mass-energy distributions occur about intersections of phase transitions that modify the shock front of global expansion, and the predicted number of galaxies approximates that determined by observation.     

Coherent Population Trapping and Partial Decoherence in the Stochastic Limit

We use the stochastic limit technique to predict a new phenomenon concerning a two-level atom with degenerate ground state interacting with a quantum field. We show, that the field drives the state of the atom to a stationary state, which is non-unique, but depends on the initial state of the system through some conserved quantities. This non uniqueness follows from the degeneracy of the ground state of the atom, and when the ground subspace is two-dimensional, the family of stationary states will depend on a one-dimensional parameter. Only one of the stationary states in this family is a pure state and it coincides with the known trapped state. This means that by controlling the initial state (input) we can control the final state (output). The quantum Markov semigroup obtained in the limit admits an invariant pure state, but it is not true that all the extremal invariant states are pure. This is an interesting phenomenon also from mathematical point of view and its meaning will be discussed in a future paper. PACS numbers: 31.15.-p, 31.15.Gy, 32.80.Pj, 32.80.Qk     

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron-phonon and the impurity ion-phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion-phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron-phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.     

Large deviations for ℤ d -Actions

We establish large deviations bounds for translation invariant Gibbs measures of multidimensional subshifts of finite type. This generalizes [FO] and partially [C, O, and B], where only full shifts were considered. Our framework includes, in particular, the hard-core lattice gas models which are outside of the scope of [FO, C, O, and B].Partially supported by US-Israel BSF. Partially sponsored by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany).     

Gibbsian Stationary Non-equilibrium States

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.     

Atmospheric channel characteristics for quantum communication with continuous polarization variables

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute’s building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.     

Noise induced patterning in reaction-diffusion systems with non-Fickian diffusion

We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. It was found that at small and large noise intensities the system is characterized by unstable homogeneous states. At intermediate values of the noise intensity three types of patterns are possible: nucleation, spinodal decomposition and stripes with liner defects (dislocations). Our analytical investigations are verified by computer simulations.     

On the stationary measures of anharmonic systems in the presence of a small thermal noise

We consider certain small stochastic perturbations of ad-dimensional infinite system of coupled anharmonic oscillators. The evolution law is reversible in the Yaglom sense, thus Gibbs states with the given interaction and temperature are stationary measures. If d<3 then some stability properties of the interaction imply the converse statement; if d>2 then the same is proven for translation invariant measures only. The methods and results of Ref. 4, 6–8 are extended to second-order systems of stochastic differential equations.     

Observation of nuclear wave packets in the excited state of the F-center in alkali halides

Oscillations of nuclear wave packets (NWPs) in the excited state of the F-center in four alkali halides, potassium chloride (KCl), potassium bromide (KBr), potassium iodide (KI), and rubidium chloride (RbCl), are investigated. In KCl, the dominant mode is the LO mode near the zone center in the Brillouin zone. In KBr, the NWP oscillation consists mainly of the LO mode near the zone center and the LA modes near the singularity points in the [1 0 0] and/or [1 1 0] crystal directions. In KI, the totally symmetric local mode is dominant in the NWP oscillation. In RbCl, the LO mode near the zone boundary [1 0 0] predominantly forms the NWP oscillation. We comprehensively elucidate correspondences and differences between the present results and the resonance Raman spectra by considering the spatial extension of the electronic wave function and the perturbed phonon density of states.     

Dynamical ensembles in nonequilibrium statistical mechanics and their representations

The stationary states of driven systems of particles are considered from the point of view of the invariant probability distributions in the phase space which characterize them. The main features of various representations of such distributions are reviewed, and a brief derivation of the one based on orbital measures is given. We mention the limits of the mathematical derivations, and discuss the expected range of applicability beyond such limits. (c) 1998 American Institute of Physics.     

The classical mechanics of one-dimensional systems of infinitely many particles

We apply the existence theorem for solutions of the equations of motion for infinite systems to study the time evolution of measures on the set of locally finite configurations of particles. The set of allowed initial configurations and the time evolution mappings are shown to be measurable. It is shown that infinite volume limit states of thermodynamic ensembles at low activity or for positive potentials are concentrated on the set of allowed initial configurations and are invariant under the time evolution. The total entropy per unit volume is shown to be constant in time for a large class of states, if the potential satisfies a stability condition.On leave from: Department of Mathematics, University of California, Berkeley, California.     

托卡马克中逃逸电子分布函数和波能密度计算

本文用非等距有限差分法,求解了准线性微分方程组,获得了在电子平行速度区间,逃逸电子分布函数和波能密度的二维演化图象。这一结果比文[1]和[2]在稳态情形下所得到的解析结果以及文[1]在一维情形下演化的解析结果,较完整地反映了逃逸电子分布函数的特征。可供对逃逸电子的进一步研究参考。     

Translation invariant tensor product states in a finite lattice system

We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from a same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.     

Improving the acoustic working conditions for musicians in small spaces

In the acoustic consulting, testing, design and engineering work of the Fraunhofer-Institute of Building Physics (IBP) the low-frequency end of the noise spectra and the room acoustic conditioning has gained tremendous importance over the years. For solving the long-ranging noise pollution from e.g. exhaust stacks and chimneys, a series of low-frequency sound attenuators with minimum flow resistance were developed. Its first representative was a novel membrane absorber [10] [Ackermann U, et al., Sound absorbers of a novel membrane construction. Applied Acoustics 1998;25:197-215]. Thanks to its slenderness and ruggedness it could also be employed for noise control and reverberation adjustment purposes in relatively narrow enclosures and harsh environments [11] and [12] [Vér IL. Enclosures and wrappings. In: Harris CM, editor. Handbook of acoustical measurements and noise control. New York: McGraw-Hill, 1991; Fuchs HV, Hunecke J. The room plays its part at low frequencies. Das Musikinstrument 1993;42:40-6 (in German). Meanwhile a new type of panel absorber has been optimized for both kinds of application. Its absorption efficiency at frequencies far below 100 Hz could be demonstrated and quantified by a special measuring procedure based on the reverberation of a small rectangular room at its eigenfrequencies [3] (Zha X, et al. Measurements of an effective absorption coefficient below 100 Hz. Acoustics Bulletin 1999;24:5-10). With the aid of this novel tool it is now possible to qualify reverberation rooms and anechoic chambers for frequencies down to 63 and 31 Hz, respectively [9] (Fuchs HV, et al. Qualifying freefield and reverberation rooms for frequencies below 100 Hz. Applied Acoustics 2000;59:303-22). In a companion paper in this same journal [4] [Fuchs HV, et al.: Creating low-noise environments in communication rooms. Applied Acoustics (in print)] appropriate experience is reported in creating low-noise environments in multi-purpose rooms like offices, restaurants, foyers and seminars. A number of representative case studies [5] (Drotleff H, et al. : Attractive acoustic design of multi-purpose halls. 1. Chinese-German Platform Innovative Acoustics 2000, (October, 21-25. 2000)) show ample evidence that the low-frequency performance of the rooms has a strong influence on both the amplification of intruding external noise and the development of internally generated noise emanating from communication processes provoked by the users themselves. At work places where producing sound (by voices or/and instruments) is the main or only purpose for their existence, the acoustic qualification of the room at low frequencies turns out to be of the utmost importance, especially when musicians are forced to work in extremely narrow spaces like orchestra pits and rehearsal halls for many hours a day and often under extreme physical and mental pressure. The measures taken and described herein have proven to mitigate if not remove some of the acoustic burden put on musicians employed in states theatres.     

Renormalization Group¶and the Melnikov Problem for PDE's

We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that was developed recently in [BGK] to address the standard KAM problem, namely, persistence of invariant tori of maximal dimension in finite dimensional, near integrable systems. Our result covers situations in which the so called normal frequencies are multiple. In particular, it provides a new proof of the existence of small-amplitude, quasi-periodic solutions of nonlinear wave equations with periodic boundary conditions. Received: 29 January 2001 / Accepted: 8 March 2001