Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics

If , and is a finite (nonabelian) group, then is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of . We characterize when MCA are group endomorphisms of , and show that MCA on inherit a natural structure theory from the structure of . We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure.     

Diffusion in a symmetric bistable potential: A variational approach

An approximation procedure for the solution of stochastic nonlinear equations, which was derived from a variational principle in a previous paper, is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium. The second moment and variance for the particle's position are calculated as functions of the timet. Good agreement is found with results recently obtained by Baibuzet al. from an approximate evaluation of a path integral expression for the probability density.     

Photoelasticity in quasicrystals

The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C₅), (S₁₀), (C_5h ), m2(D_5h ), 52(D₅), 5m(C_5v ), 2m(D_5d ); 235(I), 2/m (I _h )—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.     

Modules over\mathfrak{U}_q (\mathfrak{s}\mathfrak{l}_2 )

The restricted quantum universal enveloping algebra decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple . The indecomposable finite-dimensional are classified and located in the Auslander-Reiten quiver.     

A mathematical condition for a sublattice of a propositional system to represent a physical subsystem,with a physical interpretation

We display three equivalent conditions for a sublattice, isomorphic to aP , of the propositional systemP() of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim 3. We prove that one of them is still necessary and sufficient if dim <3. A physical interpretation of this condition is given.Wetenschappelijke medewerkers bij het Interuniversitair Instituut voor Kernwetenschappen (in het kader van navorsingsprogramma 21 EN).     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

World spinors—Construction and some applications

The existence of a topological double-covering for the GL(n, R) and diffeomorphism groups is reviewed. These groups do not have finite-dimensional faithful representations. An explicit construction and the classification of all (n, R), n=3,4 unitary irreducible representations is presented. Infinite-component spinorial and tensorial fields, “manifields”, are introduced. Particle content of the ladder manifields, as given by the (3, R) “little” group, is determined. The manifields are lifted to the corresponding world spinorial and tensorial manifields by making use of generalized infinite-component frame fields. World manifields transform w.r.t. corresponding representations, which are constructed explicitly. Supported in part by the Science Foundation (Belgrade).     

A remark on extensions of quasi-free derivations on the CAR-algebra

Let δ be a quasi-free derivation of the CAR algebra, and let be a closed *-derivation which is an extension of δ. We use Price's techniques from [6] to show that if the polynomials in the linear field operators a(f)→a ^* (f) in D( ) is a core for , then is quasi-free.     

Bound States in a Locally Deformed Waveguide: The Critical Case

We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c ₁,c ₂ suchthat the corresponding eigenvalue satisfies for all sufficiently small.     

Comment on “Evaluation of concentration-depth profiles by sputtering in SIMS and AES” by S. Hofmann

The statistics of the sputtering process, which has been used to explain sputterbroadening effect due to surface roughness, has been treated with conditional probabilities. This results in the relationship, , instead of derived by S. Hofmann [Appl. Phys.9, 59 (1976)], where δz,z, and are the depth resolution, sputtered depth and sputtering yield, respectively.     

Regularized,continuum Yang-Mills process and Feynman-Kac functional integral

Giving an ultraviolet regularization and volume cut off we construct a nuclear Riemannian structure on the Hilbert manifold of gauge orbits. This permits us to define a regularized Laplace-Beltrami operator on and an associated global diffusion in governed by . This enables us to define, via a Feynman-Kac integral, a Euclidean, continuum regularized Yang-Mills process corresponding to a suitable regularization (of the kinetic term) of the classical Yang-Mills Lagrangian onT .On leave of absence from Zaragoza University (Spain)Laboratoire associé au CNRS     

A Zakharov-Shabat inverse scattering problem with a polynomial spectral dependence in the potential

The inverse scattering problem for the Zakharov-Shabat system , is considered. It is solved by reduction to the inverse scattering problem for two coupled Zakharov-Shabat systems in a 4n-dimensional space: . This work has been done as part of the program ‘Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses’. Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.     

Superconformal current algebras and their unitary representations

A natural supersymmetric extension is defined of the current (= affine Kac-Moody Lie) algebra ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of are constructed. They extend to unitary representations of the semidirect sumS (G) of with the superconformal algebra of Neveu-Schwarz, for , or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria     

Bethe subalgebras in twisted Yangians

We study analogues of the Yangian of the Lie algebra for the other classical Lie algebras and . We call them twisted Yangians. They are coideal subalgebras in the Yangian of and admit homomorphisms onto the universal enveloping algebras U( ) and U( ) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U( ) and U( ) of these subalgebras are also maximal commutative.     

Covariance algebras in field theory and statistical mechanics

Starting from aC*-algebra and a locally compact groupT of automorphisms of we construct a covariance algebra with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of i.e. *-representations of in which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebra yielding the *-representations of in which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of . Finally we consider the covariance algebra built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.On leave of absence from Istituto di Fisica G. Marconi — Roma.     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form

It is shown that for normal states ρ and φ of a W ^*-algebra , where P(.,.) is the transition probability considered by Uhlmann [1], and ζ(ω) is the vector in the natural positive cone of some standard faithful representation of A, associated with the normal state ω. The above inequality is equivalent to: , where d(.,.) is the Bures distance function [5].     

Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

We consider stochastic processes, with finite, in which spin flips (i.e., changes of S ^t _x ) do not raise the energy. We extend earlier results of Nanda–Newman–Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.