Colored noise in activated rate processes

We consider bistable systems driven by stationary wideband Gaussian colored noise. We construct uniform asymptotic expansions of the stationary probability density function and of the activation rate, for small intensity and short correlation time of the noise. We find that for different values of the total power output / of the noise, different terms in the asymptotic expansions become dominant. For we recover previously derived results, while for =O() and new results are obtained.     

Lp-Spaces for UHF Algebras

We construct L^p-spaces for a UHFalgebra A with a faithful product state . We showthat the spaces obtained are isomorphic, as Banachspaces, to the Haagerup spaces L^p((A)).     

Neutron-proton bremsstrahlung atE=76 MeV

We compare the electric and pure magnetic contributions to the differential cross sectiond(npnp)/ds' of neutron-proton bremsstrahlung. We conclude that the pure magnetic contribution cannot explain the discrepancy between the theoretical and experimental results as found by Dupont et al.This work was supported in part by CONACyT under contracts F246-E9207 and 1628-E9209     

Lévy walks for turbulence: A numerical study

We present a numerical study of enhanced diffusion, for which the mean-squared displacement follows asymptotically r ²(t) t , > 1. We simulate continuous time random walks with waiting-time distributions which couple the spatial and temporal parameters; this gives rise to Lévy-walks. Our results confirm the theoretically predicted long-time behavior and demonstrate its temporal regime of validity. Furthermore, the simulations document the appearance of (parameter-dependent) transitions between regular and enhanced diffusion regimes.     

“Principle of Indistinguishability” and Equations of Motion for Particles with Spin

In this work we review the derivation of Dirac and Weinberg equations based on a principle of indistinguishability for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG for a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j= , there exists no Dirac-like equation for the (j,0)(0,j) representation nor for the ( , ) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)( , )(0,1) representation by this method and show that the (1, )( ,1) representation satisfies a Dirac-like equation which describes a multiplet of with masses m and m/2, respectively.     

Noncommutative Riemannian and Spin Geometry of the Standard <Emphasis Type="Italic">q</Emphasis>-Sphere

We study the quantum sphere as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum ^0,11,0 in a double complex. We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators and projective module structure. We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci curvature and q-Dirac operator . We find the possibility of an antisymmetric volume form quantum correction to the Ricci curvature and Lichnerowicz-type formulae for We also remark on the geometric q-Borel-Weil-Bott construction.     

The limits of Brans-Dicke spacetimes: a coordinate-free approach

We investigate the limit of Brans-Dicke spacetimes applying a coordinate-free technique. We obtain the limits of some known exact solutions. It is shown that these limits may not correspond to similar solutions in the general relativity theory.     

Temperature in Friedmann thermodynamics and its generalization to arbitrary space-times

In recent articles we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models were treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential, etc.). This model has the advantage of allowing us to determine the geometry of the universe by thermodynamic stability arguments. In this paper, in search for evidence for the definition of gravitational temperature, we will investigate a massless conformal scalar field in an Einstein universe in detail. We will argue that the gravitational temperature of the Einstein universe is given asT _g=1/2) (c/k) (1/R ₀), where R₀ is the radius of the Einstein universe. This is in accord with our definition of gravitational temperature in Friedmann thermodynamics and determines the dimensionless constant as 1/2. We discuss the limitations of the model we are using. We also suggest a method to generalize our gravitational temperature to arbitrary space-times granted that they are sufficiently smooth.Based on three essays awarded honorable mention in the years 1987, 1988 and 1989 by the Gravity Research Foundation—Ed.     

The string model for ultrarelativistic nuclear scattering

We review basic theoretical concepts to describe nuclear collisions at ultrarelativistic energies. We discuss relativistic strings, Gribov-Regge theory (GRT) of hadronic interactions and string models based on GRT, and finally generalizations to nucleus-nucleus scattering.Invited lecture given at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.     

A lower bound for the memory capacity in the Potts-Hopfield model

We consider Potts-Hopfield networks of sizeN. We prove the result: _c >0 such that for all 0<< _c we can find, >0 in such a way that, whenN, we can store N patterns, all of them being sorrounded by -energy barriers at distance.     

Interpolating gauges and the importance of a careful treatment of ε-term

We consider the use of interpolating gauges (with a gauge function F[A;]) in gauge theories to connect the results in a set of different gauges in the path-integral formulation. We point out that the results for physical observables are very sensitive to the epsilon term that we have to add to deal with singularities and thus it cannot be left out of a discussion of gauge-independence generally. We further point out, with reasons, that the fact that we can ignore this term in the discussion of gauge independence while varying of the gauge parameter in Lorentz-type covariant gauges is an exception rather than a rule. We show that generally preserving gauge-independence as is varied requires that the -term has to be varied with . We further show that if we make a naive use of the (fixed) epsilon term (that is appropriate for the Feynman gauge) for general interpolating gauges with arbitrary parameter values [i.e. ], we cannot preserve gauge independence [except when we happen to be in the infinitesimal neighborhood of the Lorentz-type gauges]. We show with an explicit example that for such a naive use of an -term, we develop serious pathological behavior in the path-integral as is/are varied. We point out that correct way to fix the -term in a path-integral in a non-Lorentz gauge is by connecting the path-integral to the Lorentz-gauge path-integral with correct -term as has been done using the finite field-dependent BRS transformations in recent years.     

On the Long Time Behavior of Infinitely Extended Systems of Particles Interacting via Kac Potentials

We analyze the long time behavior of an infinitely extended system of particles in one dimension, evolving according to the Newton laws and interacting via a non-negative superstable Kac potential (x)=(x), (0, 1]. We first prove that the velocity of a particle grows at most linearly in time, with rate of order . We next study the motion of a fast particle interacting with a background of slow particles, and we prove that its velocity remains almost unchanged for a very long time (at least proportional to ^–1 times the velocity itself). Finally we shortly discuss the so called Vlasov limit, when time and space are scaled by a factor .     

Borel summability of the mass and theS-matrix in ϕ4 models

We show that in the ₂ ⁴ theory, the physical mass and the two-bodyS-matrix are Borel summable in the coupling constant at =0.     

Interfacial properties in solid-stabilized emulsions

We prepared concentrated monodisperse oil-in-water emulsions stabilized by solid particles. The osmotic resistance, , of the emulsions was measured for different oil volume fractions above the random close packing ( ). The dimensionless osmotic resistance, /(/R) ( being the interfacial tension and R being the undeformed drop radius), was always substantially higher than the corresponding values obtained for surfactant-stabilized emulsions. It can be concluded that droplet deformation in solid-stabilized emulsions is not controlled by the capillary pressure, /R, of the non-deformed droplets but rather by 0/R, 0 being a parameter characterizing the rigidity of the droplets surfaces. The data can be interpreted considering that the interfacial layers are elastic at small deformations and exhibit plasticity at intermediate deformations. 0 corresponds to the surface yield stress, i.e. the transition between elastic and plastic regimes. We discuss the origin of the surface behavior considering the strong lateral interactions that exist between the adsorbed solid particles. We propose an independent measurement of 0 based on the critical bulk stress that produces droplet fragmentation in dilute emulsions submitted to shear. Finally, the bulk shear elastic modulus was measured as a function of and confirms many of the features revealed by the osmotic resistance.     

Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

The 1/N F expansion of the γ and β functions in Q.E.D.

The Callan-Symanzik- and-functions are calculated analytically for Q.E.D. in the limit of a large number of leptons (N _F) up to terms of order 1/N _F inclusive. We give closed analytic expressions for the coefficients of these terms in their series expansion in powers ofK N _F/. We have been able to sum these series and to obtain some striking results.     

State Property Systems and Closure Spaces: A Study of Categorical Equivalence

We show that the natural mathematical structureto describe a physical entity by means of its states andits properties within the Geneva–Brussels approachis that of a state property system. We prove that the category of state property systems (andmorphisms) SP is equivalent to the category ofclosure spaces (and continuous maps) Cls. We showthe equivalence of the state determinationaxiom for state property systems with the T₀separation axiom for closure spaces. We alsoprove that the category SP ₀ ofstate-determined state property systems is equivalent tothe category L ₀ of based completelattices. In this sense the equivalence of SP andCls generalizes the equivalence ofCls ₀ (T₀ closure spaces)and L ₀ proven by Erne(1984).     

On foundation of the generalized Nambu mechanics

We outline basic principles of a canonical formalism for the Nambu mechanics—a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of a Nambu bracket, which generalizes the Poisson bracket—a binary operation on classical observables on the phase space—to the multiple operation of higher ordern3. Nambu dynamics is described by the phase flow given by Nambu-Hamilton equations of motion—a system of ODE's which involvesn–1 Hamiltonians. We introduce the fundamental identity for the Nambu bracket—a generalization of the Jacobi identity—as a consistency condition for the dynamics. We show that Nambu bracket structure defines a hierarchy of infinite families of subordinated structures of lower order, including Poisson bracket structure, which satisfy certain matching conditions. The notion of Nambu bracket enables us to define Nambu-Poisson manifolds—phase spaces for the Nambu mechanics, which turn out to be more rigid than Poisson manifolds—phase spaces for the Hamiltonian mechanics. We introduce the analog of the action form and the action principle for the Nambu mechanics. In its formulation, dynamics of loops (n–2-dimensional chains for the generaln-ary case) naturally appears. We discuss several approaches to the quantization of Nambu mechanics, based on the deformation theory, path integral formulation and on Nambu-Heisenberg commutation relations. In the latter formalism we present an explicit representation of the Nambu-Heisenberg relation in then=3 case. We emphasize the role ternary and higher order algebraic operations and mathematical structures related to them play in passing from Hamilton's to Nambu's dynamical picture.     

Universal expansion of the powers of a derivation

We give the expansion of the powers of the Lie operator = ⁱ _i in any dimension, where is either a smooth function or a formal power series over an infinite set of commutatives indeterminates. We describe an algorithm for computer treatment and we give, as an example, a table for the orders 1 to 6.     

Is Indistinguishability in Quantum Mechanics Conventional?

Darrin Belousek has argued that the indistinguishability of quantum particles is conventional in the Duhemian–Einsteinian sense, in part by critially examining prior arguments given by Redhead and Teller. Belousek's discussion provides a useful occasion to clarify some of those arguments, acknowledge respects in which they were misleading, and comment on how they can be strengthened. We also comment briefly on the relevant sense of conventional.