Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber ratec(s; x) at sitex when the configuration iss satisfies detailed balance at temperatureT, while the Kawasaki ratec(s; x, y) between nearest-neighbor sitesx andy satisfies detailed balance at a different temperatureT. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values forT,T, and; this generalizes previous analytical and numerical studies for and/orT. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.Dedicated to Joel L. Lebowitz on the occasion of his 60th birthday.     

Proton spin-lattice relaxation times in ytterbium hydrides

The measurements of the proton (NMR) spinlattice relaxation times have been made in a series of ytterbium hydrides, YbH _x . Results are reported forx=1.80, 1.95, 2.00 and 2.62 and temperatures 4.2T297K. In the orthorhombic phase (1.80x2.00), the spin-lattice relaxation times are dominated by the hyperfine interaction of protons with conduction electrons and the spin diffusion mechanism. In the cubic phase (x=2.62), the relaxation times are five orders of magnitude shorter than in the orthorhombic one. This is interpreted in terms of the proton coupling with the Yb³⁺ ion spin fluctuations.     

The electronic structure of the mixed 5f system UC x N1−x

We present results of electronic structure calculations for UC _x N_1–x obtained with the relativistic Korringa-Kohn-Rostocker Greens function (RKKR-GF) method. While on the anion sites the disorder is treated within the Coherent Potential Approximation (CPA) the small change in the cation potential upon alloying is accounted for in the averaget-matrix approximation (ATA). The presence of strong local spin fluctuations forx0.6 restricts our treatment to the carbon rich phase, and even there we find that the observed linear specific heat coefficient is much enhanced over the bandstructure value. The computed X-ray photoemission spectra vary smoothly with composition the main change consisting in the melting away of the side peak at –3 eV binding energy seen in pure UC with the adjunction of nitrogen.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Theory of fiber bundle with local metric of internal space and gravitation with torsion

In this paper we propose a new theory of a fiber bundle provided with a local metric of internal space. The fibers differ from usual fibers, having an enlarged factor. The enlargement may be procured by a differential mapping(x) from structure groupG to the fiberF _x atx M, and(x)R. The torsion presented stems from the local metric of internal space and the local metric stems from a induced mapping _*(x) of(x). From the theory we can get the Brans-Dicke theory with torsion. If we assume the spin density of the gauge field determines the enlarged factor of the fiberF _x, our theory is an extended Cartan theory.     

Spin glasses with long-range interaction at high temperatures

We study the Ising andN-vector spin glasses with exchange couplings J=(J _ij ;i, jZ ^d ), which are independent random variables with EJ_ij=0 andEJ ⁿ _ij ⁿ n!¦i–j¦ ^–nd , forn, some finite constant >0, and >1/2. For sufficiently small, we show that forE-a.a.J there is a weakly unique, extremal, infinite-volume Gibbs measure _J for which the expectation of a single (component of) spin vanishes and which has the cluster property inL ₂(E) with the same decay as interaction. This work is based on results and methods of Fröhlich and Zegarlinski.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Some consequences of the nonlocalizability of space-time events

Space-time events are characterized by their coordinatesx from the classical point of view. The same events from the quantum-mechanical point of view should be described rather by the expectation value of coordinates X. The expectation value could be evaluated by introducing a density operator(x,x) associated with the event. In the case where(x,x) cannot be described by delta functions strictly monochromatic radiation does not exist. If localizability is limited by Planck's length there are no narrower spectral lines than 2× 10^–29 E ² (eV) whereE stands for the photon energy.On leave from the Institute of Nuclear Physics, Kraków, ul. Radzikowskiego 152, Poland.     

Inverse Problem for Harmonic Oscillator Perturbed by Potential,Characterization

Consider the perturbed harmonic oscillator Ty=-y+x²y+q(x)y in L²(), where the real potential q belongs to the Hilbert space H={q, xq L²()}. The spectrum of T is an increasing sequence of simple eigenvalues _n(q)=1+2n+_n, n 0, such that _n 0 as n. Let _n(x,q) be the corresponding eigenfunctions. Define the norming constants _n(q)=lim_xlog |_n (x,q)/_n (-x,q)|. We show that for some real Hilbert space and some subspace Furthermore, the mapping :q(q)=({_n(q)}₀, {_n(q)}₀) is a real analytic isomorphism between H and is the set of all strictly increasing sequences s={s_n}₀ such that The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -ypy, p L²(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces We obtain their basic properties, using their representation as spaces of analytic functions in the disk.     

The heat semigroup and integrability of Lie algebras: Lipschitz spaces and smoothness properties

We define and analyze Lipschitz spaces _,q associated with a representationxgV(x) of the Lie algebrag by closed operatorsV(x) on the Banach space together with a heat semigroupS. If the action ofS satisfies certain minimal smoothness hypotheses with respect to the differential structure of (,g,V) then the Lipschitz spaces support representations ofg for which productsV(x)V(y) are relatively bounded by the Laplacian generatingS. These regularity properties of the _,q can then be exploited to obtain improved smoothness properties ofS on . In particularC ₄-estimates on the action ofS automatically implyC -estimates. Finally we use these results to discuss integrability criteria for (,g,V).Dedicated to Res Jost and Arthur Wightman     

Noncommutative Ricci Curvature and Dirac Operator on C q [SL2] at Roots of Unity

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group C _q [ SL₂], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for q an odd rth root of unity that its eigenvalues are given by q-integers [m] _q for m=0,1...,r–1 offset by the constant background curvature. We fully solve the Dirac equation for r=3.     

Properties of yttrium-iron-metalloid glasses

We report the results of measurements on metallic glasses of the form Y₆₆(Fe_1–x M _x )₃₄. For M = B we find that there is an extended range of glass formation (0x0.40) and that properties such as atomic density, electrical resistivity, microhardness, and thermal stability are functions ofx. For M = C, Si, or Ge we find a restricted range of glass formation (0 x0.10) and no significant changes in the properties of the glasses. Using Fe⁵⁷ Mössbauer effect spectroscopy we find that the M = B case is again unique in that the structure of the glass is sensitive to B content. We relate the differences in glass formation for the M = B and M = C, Si, Ge glasses to the existence of Y rich compounds in the C, Si, and Ge cases and the lack of such compounds in the M = B case.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

T-invariance of relativistic first-order equations

We consider the time-inversion operation for relativistic first-order equations that are constructed without the use of multiple representations of the proper Lorentz group. It is proved that the matrix T of the antilinear time-inversion operation is symmetric (antisymmetric) for particles with integral (half-integral) spin. It is shown that for particles with integral (half-integral) spin there exists (does not exist) a linear transformation as a result of which the time-inversion operation reduces to the complex conjugate:(x)= _T ^*(x) where _T is a phase factor. A general expression for such a transformation is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 5–9, December, 1988.     

Magnetic field alignment of high-T c superconductorsRBa2Cu3O7–δ (R=rare earth)

Finely ground powders ofRBa₂Cu₃O_{7 –} (R=Y, Nd, Sm, Eu, Dy, Ho, Er, Tm, Yb) have been mixed at dilute 3%-by-volume concentrations into epoxy matrices which were then allowed to harden in applied magnetic fieldsH _A=18 kOe. X-ray diffractometry studies and 4.3 K measurements of supercurrent-induced magnetization hysteresisM are interpreted as indicating at least partial alignment of single-crystal-grain c-axes (1) parallel toH _A forR=Y, Nd, Sm, Dy, Ho (as earlier found by Farrell et al. forR=Y), and (2) perpendicular toH _A forR=Eu, Er, Tm, Yb. With a few exceptions (Y, Sm, Eu) the alignment direction correlates with the sign of the second-order Stevens factor _J of the crystalline electric field Hamiltonian in the manner suggested by Livingston et al. For the best aligned specimens (Ho, Dy) critical current densitiesJ _c (4.3 K, 5 kOe) for individual grains are estimated fromM and the Bean model to be of order 10⁷ A/cm² for the measuring fieldH parallel to the original alignment fieldH _A, and of order 10⁶ A/cm² forH perpendicular toH _A.     

Inertial range spectrum of a fractal model for turbulence

The present study deals with a model for 3D turbulence which is based on a fractal set ink-space (massM(k)logk, i.e.d _f=0). The energy spectrumE(_k) is calculated by a method similar to the Monte Carlo renormalization technique of Ma [1]. To apply this we decouple the set into next-neighbour pairs of energy shells.E _k is calculated iteratively by simulating the pairs. Their rough scales are forced and their fine scales are damped by an eddy viscosity ^e. We start in the viscous range where ^e is neglected. An intertial range shows up with a spectrumE(k)k^–, =1.68±0.07, and an eddy viscosity ^e(k)k ^-,=1.3±. The possible benefit for the simulation of turbulent flows is pointed out.