Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases

A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity () plane at =0, whereas in the insulating phase a neighborhood of =0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless coupling, the zeros pinch the point =0 for<2, while for2 a neighborhood of =0 is zero free. The conductor-insulator transition therefore takes place at=2 independent of the density and other parameters in the model.     

Integration in the GHP Formalism IV: A New Lie Derivative Operator Leading to an Efficient Treatment of Killing Vectors

In order to achieve efficient calculations and easy interpretations of symmetries, a strategy for investigations in tetrad formalisms is outlined: work in an intrinsic tetrad using intrinsic coordinates. The key result is that a vector field is a Killing vector field if and only if there exists a tetrad which is Lie derived with respect to ; this result is translated into the GHP formalism using a new generalised Lie derivative operator with respect to a vector field . We identify a class of it intrinsic GHP tetrads, which belongs to the class of GHP tetrads which is generalised Lie derived by this new generalised Lie derivative operator in the presence of a Killing vector field . This new operator also has the important property that, with respect to an intrinsic GHP tetrad, it commutes with the usual GHP operators if and only if is a Killing vector field. Practically, this means, for any spacetime obtained by integration in the GHP formalism using an intrinsic GHP tetrad, that the Killing vector properties can be deduced from the tetrad or metric using the Lie-GHP commutator equations, without a detailed additional analysis. Killing vectors are found in this manner for a number of special spaces.     

Correlated majority model

We extend the bichromatic majority model by including (one-dimensional isotropic) correlations and numerically discuss, through Monte Carlo simulations, the simple, 1/3, and 2/3 majority rules. We calculate, as functions of the concentration and correlation degree, the mean finite cluster size, and the order parameterm as well as their respective critical exponents and. We find1 regardless of the correlation degree or the type of majority. Also, a supplementary divergence of is observed at the>0 borderline.     

Functional Realization and Nonlinear Induced Representation in the Geometrodifferential Conception of Extended Particles

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables , a physical wave _x () representing the proper characteristics of the particles, and a functional wave X [ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The first study is undertaken in a special instance _x () = (x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Renormalization group equations with several length scales and crossover scaling functions for axial anisotropy

The critical behaviour of axially anisotropicn-vector models is characterized by two distinct length scales, the correlation lengths and for the easy and hard axes. In order to handle the full range of anisotropics from to partial differential renormalization group equations are derived, depending on and . The anisotropicX-Y model is studied in detail near four dimensions. The crossover scaling functions for the susceptibilities are calculated to first order in=4–d. Two distinct crossover regions are found for weak and dominant anisotropy, respectively.     

Transport properties of the continuous-time random walk with a long-tailed waiting-time density

We derive asymptotic properties of the propagatorp(r,t) of a continuous-time random walk (CTRW) in which the waiting time density has the asymptotic form(t)T /t ⁺¹ whentT and 0<<1. Several cases are considered; the main ones are those that assume that the variance of the displacement in a single step of the walk is finite. Under this assumption we consider both random walks with and without a bias. The principal results of our analysis is that one needs two forms to characterizep(r,t), depending on whetherr is large or small, and that the small-r expansion cannot be characterized by a scaling form, although it is possible to find such a form for larger. Several results can be demonstrated that contrast with the case in which t= ₀ ()d is finite. One is that the asymptotic behavior ofp(0,t) is dominated by the waiting time at the origin rather than by the dimension. The second difference is that in the presence of a fieldp(r,t) no longer remains symmetric around a moving peak. Rather, it is shown that the peak of this probability always occurs atr=0, and the effect of the field is to break the symmetry that occurs when t. Finally, we calculate similar properties, although in not such great detail, for the case in which the single-step jump probabilities themselves have an infinite mean.     

On the Born-Oppenheimer approximation for excited states of polyatomic Schrödinger operators

In this Letter, excited states of polyatomic molecular Schrödinger operators are investigated with the help of the Born-Oppenheimer approximation. The ratio of electronic and nuclear mass plays the role of a semi-classical parameter h ². Asymptotic series of eigenvalues at the bottom of the spectrum are constructed up to any order in h. Mathematically, this leads to the discussion of the semi-classical limit of pseudo-differential operators with the principal symbol po(x,) = ² + , where has a degenerate minimum (a whole manifold).     

Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt {1 + l^4 R^2 }

We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian _EH = R/16G and a pure cosmological constant for large R with the ansatz _cs = _EH/ , where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by d/dR = 1/16G _eff is G _eff = G , and tends to infinity for large R, in contrast to most other approaches where G _eff 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds ² = a ² [da ²/B(a) – dx ² – dy ² – dz ²] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R ± are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein's theory. In synchronized time, the metric is given by

The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.     

Lorentzian Warped Products and Singularity

We show that to any convex function f: ⁿ there correspondinfinitely many geodesically complete metricsds² such that Ric() 0 for anynonspacelike vector . These metrics are constructedas the warped products of the natural metric in and the inner metric of a convexhyperface (the graph of f) in ^{n + 1}.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

A Kerr-NUT metric

Using Galilean time and retarded distance as coordinates the usual Kerr metric is expressed in form similar to the Newman-Unti-Tamburino (NUT) metric. The combined Kerr-NUT metric is then investigated. In addition to the Kerr and NUT solutions of Einstein's equations, three other types of solutions are derived. These are (i) the radiating Kerr solution, (ii) the radiating NUT solution satisfyingR _ik= _{i k} , _i ⁱ = 0, and (iii) the associated Kerr solution satisfyingR _ik=0. Solution (i) is distinct from and simpler than the one reported earlier by two of us (P.C.V.; L.K.P) [6]. Solutions (ii) and (iii) give line elements which have the axis of symmetry as a singular line.     

New extended model of the Dirac electron

Using a nonlocal function (y)= K (|y –x|)(x) d(x) as a solution of the Dirac equation, we have constructed a new extended model of Dirac's electron. This new model of the electron permits us to eliminate all known divergences in a natural way. The fundamental role of an elementary length (which can be calculated) in the treatment of divergences is presented in detail. The essential feature of the model is the hypothesis of the existence of an electron which possesses a center of charge and a center of mass that do not coincide. Finally, a calculation of the fine structure constant =e ²/hc based on such a model is presented.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

The dependence of the uniaxial magnetic anisotropy in evaporated films on the angle of incidence

The method of local ferromagnetic resonance and direct torsional measurements were used to measure the dependence of the magnetic anisotropy in permalloy films on the angle of incidence in a broad range of such angles. It was found that this dependence is not monotonous and that at larger angles of incidence the easy axis of magnetization is rotated. An interpretation of this phenomenon is proposed.

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In conclusion the authors wish to thank J. Grolmus for performing some of the measurements, members of the mechanics workshop of the Institute of Physics, Czechoslovak Academy of Sciences, for carefully preparing the apparatus, and particularly K. Schaffner for accurately making the resonance cavity. We thank J. Kaczér and V. Janovec for carefully reading this paper and for a number of valuable remarks.     

Основные соотношени я длн построения механических селект оров нейтронов

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The scattering of waves by a periodic surface

The paper derives a general formula for the scattering of electromagnetic (or sound) waves from a periodic, perfectly conducting (or perfectly rigid) surface. No restrictions are imposed on the angle of incidence, the size of the surface or the degree of roughness. Except for the basic Kirchhoff approximation, the method is exact. The results confirm, generalise or correct special cases obtained by more complicated methods.

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Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.