The Oscillator Representation and¶Groups of Heisenberg Type

We obtain the explicit reduction of the Oscillator representation of the symplectic group, on the subgroups of automorphisms of certain vector-valued skew forms | of "Clifford type"-equivalently, of automorphisms of Lie algebras of Heisenberg type. These subgroups are of the form G · \Spin(k), with G a real reductive matrix group, in general not compact, commuting with Spin(k) with finite intersection. The reduction turns out to be free of multiplicity in all the cases studied here, which include some where the factors do not form a Howe pair. If G is maximal compact in G, the restriction to K · \Spin(k) is essentially the action on the symmetric algebra on a space of spinors. The cases when this is multiplicity-free are listed in [R]; our examples show that replacing K by G does make a difference. Our question is motivated to a large extent by the geometric object that comes with such a |: a Fock-space bundle over a sphere, with G acting fiberwise via the oscillator representation. It carries a Dirac operator invariant under G and determines special derivations of the corresponding gauge algebra.     

Large Time Behavior of¶Schrödinger Heat Kernels and Applications

We obtain global in time and qualitatively sharp bounds for the heat kernel G of the Schrödinger operator mj +V. The potential V satisfies V(x)~- C/d(x)^b near infinity with b ] (0, 2). When V S 0 our result can be described as follows: G is bounded from above and below by the multiples of standard Gaussians with a weight function. If b>2 then the weight is bounded between two positive {\it constants}; if b=2, the weight is bounded between two positive functions of t, d(x) and d(y), which have polynomial decay; if b<2, the weight is bounded between two positive functions of t, d(x) and d(y), which have exponential decay. Up to now satisfactory bounds for heat kernels can only be found when b>2 or b<0. An application to a semilinear elliptic problem is also given.     

The W-boson mass and precision tests of the Standard Model

We have examined the electroweak radiative corrections in the LEP precision data in view of the new measurements of M_W and m_t as well as the recent progress in the higher order radiative corrections. From the minimal L²-fit to the experimental Z-decay parameters (with the aid of a modified ZFITTER program), we predict that M_W=80.29(4)(2)rGeV where the first error is due to the uncertainty in the fitted m_t for a fixed m_H and the second error comes from the m_H in the range 60􊖸rGeV, which is to be compared with the current world average M_W=80.23(18)rGeV. The current world average value of M_W and the 1994 LEP data definitely favor nonvanishing electroweak radiative corrections and are consistent with a heavy m_t as measured by the recent CDF report but with a heavy Higgs scalar of about 400rGeV within the context of the minimal standard model. The sensitivity of and the errors in the best fit solutions due to the uncertainties in the gluonic coupling !_s(M_Z) and !(M_Z) are also studied carefully. In addition we discuss how the future precision measurements of M_W can provide a decisive test for the standard model with radiative corrections and give a profound implication for the measurement of t-quark and Higgs masses.     

On Chern–Simons and WZW Partition Functions

Direct analysis of the path integral reduces partition functions in Chern-Simons theory on a three-manifold M with group G to partition functions in a WZW model of maps from a Riemann surface ‡ to G. In particular, Chern-Simons theory on S³, S¹ 2 ‡, B³ and the solid torus correspond, respectively, to the WZW model of maps from S² to G, the G/G model for ‡, and Witten's gauged WZW path integral Ansatz for Chern-Simons states using maps from S² and from the torus to G. The reduction hinges on the characterization of {\cal A / G}_{n}$, the space of connections modulo those gauge transformations which are the identity at a point n, as itself a principal fiber bundle with affine-linear fiber.     

A scaling for the c-axis resistivity of La1.86Sr0.14CuO4 as a function of temperature, field and field orientation

The c-axis resistivity, A_c(T,rH,r/), of La_1.86 Sr_0.14CuO₄ is experimentally studied as a function of temperature T, magnetic field H and angle / between H and ab-plane. It is argued that the experimental findings cannot be accounted for by previously considered mechanisms. By contrast, they can be explained by a phenomenological model, which is developed by replacing H in the dissipation model for HÁIÁc with the reduced field h=H(sin²/+cos²//%²)^1/2, where % is the anisotropic parameter in magnetic fields. Based on this phenomenological model, it is shown that all the measured A_c(T,rH,r/) curves could consistently map onto a single curve.     

Influence of the substrate voltage on the random telegraph signal parameters in submicron n-channel metal-oxide-semiconductor field-effect transistors under a constant inversion charge density

In this paper, the impact of the substrate bias U_BS on the parameters of a repulsive random telegraph signal in an n-channel metal-oxide-semiconductor field-effect transistor is studied. Particular attention is paid to the variation of the capture time constant F_c with the channel current I in linear operation. It is shown that the strong reduction of F_c with I can be explained by the Coulomb blockade effect. The corresponding Coulomb energy (E of the charged-near-interface oxide trap is shown to be a strong function of the substrate bias. From the analysis of the experimental results considering surface quantization effects follows that the variation of (E with U_BS is caused by the change in both the inversion layer surface charge density N_s and in the surface electric field F_s that influences the distance between the centroid of the inversion layer and the interface. In fact, it will be demonstrated that (E can be expressed in function of a single parameter (N_sF_s²). Finally, the impact of the substrate bias on the other parameters, i.e., the amplitude (I, the emission time constant F_e and the distance d of the trap from the interface, will also be addressed.     

Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles

We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers M^N of a positive holomorphic Hermitian line bundle L over a compact complex manifold M. Our first result concerns "random" sequences of sections. Using the natural probability measure on the space of sequences of orthonormal bases {S^N_j} of H⁰(M, L^N), we show that for almost every sequence {S^N_j}, the associated sequence of zero currents &1/NZ_S^N_j; tends to the curvature form y of L. Thus, the zeros of a sequence of sections s_N ] H⁰(M, L^N) chosen independently and at random become uniformly distributed. Our second result concerns the zeros of quantum ergodic eigenfunctions, where the relevant orthonormal bases {S^N_j} of H⁰(M, L^N) consist of eigensections of a quantum ergodic map. We show that also in this case the zeros become uniformly distributed.     

Influence of the size of the interpolated cation upon the CMR properties of the perovskites Nd0.7Ca0.3−xSrxMnO3−δ

The systematic study of the manganese perovskite Nd_0.7Ca_0.3-xSr_xMnO_3-' has allowed colossal magnetoresistance effects (CMR) with resistance ratios (RR), R_B=0/R_B=5T, up to 10⁴ at 60rK in a field of 5 tesla to be evidenced. The influence of the mean size of the interpolated cation (Nd, Ca, Sr), on the magnitude of the RR ratios, has been demonstrated for the first time: RR goes through a maximum for a particular value of the mean radius of the interpolated cation. This effect seems to be correlated with the evolution of the cell volume that exhibits a singular point around x=0.085. A second important feature deals with the irreversibility of the CMR effect at low temperature that decreases as T increases and disappears at T_max. It is also remarkable that for A(T) curves characterized by a maximum, T_max not only increases as the size of the interpolated cation increases, but also as the magnitude of the applied magnetic field increases.     

N Dependence of Upper Bounds of Critical Temperatures of 2D O(N) Spin Models

We investigate critical temperature of the classical O(N) spin model in two dimensions. We show that if N is large and there is a phase transition in the system, the critical inverse temperature g_c obeys the bound g_c(N)> const. N log N.     

Solutions of the Dirac–Fock Equations for Atoms¶and Molecules

The Dirac-Fock equations are the relativistic analogue of the well-known Hartree-Fock equations. They are used in computational chemistry, and yield results on the inner-shell electrons of heavy atoms that are in very good agreement with experimental data. By a variational method, we prove the existence of infinitely many solutions of the Dirac-Fock equations "without projector", for Coulomb systems of electrons in atoms, ions or molecules, with Z h 124, N h 41, N h Z. Here, Z is the sum of the nuclear charges in the molecule, N is the number of electrons.     

From Path Representations to Global Morphisms for a Class of Minimal Models

We construct global observable algebras and global DHR morphisms for the Virasoro minimal models with central charge c(2,q), q odd. To this end, we pass from the irreducible highest weight modules to path representations, which involve fusion graphs of the c(2,q) models. The paths have an interpretation in terms of quasi-particles which capture some structure of non-conformal perturbations of the c(2,q) models. The path algebras associated to the path spaces serve as algebras of bounded observables. Global morphisms which implement the superselection sectors are constructed using quantum symmetries: We argue that there is a canonical semi-simple quantum symmetry algebra for each quasi-rational CFT, in particular for the c(2,q) models. These symmetry algebras act naturally on the path spaces, which allows to define a global field algebra and covariant multiplets therein.     

On the Magnetization of a Charged Bose Gas¶in the Canonical Ensemble

Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side L S 1 and subjected to a constant magnetic field B p 0. If the bulk density of particles A and the temperature T are fixed, then define the canonical magnetization as the partial derivative with respect to B of the reduced free energy. Our main result is that it admits thermodynamic limit for all strictly positive A, T and B. It is also proven that the canonical and grand canonical magnetizations (the last one at fixed average density) are equal up to the surface order corrections.     

Hadronic weak decays of heavy mesons and nonfactorization

The parameters L_1,2, which measure nonfactorizable soft gluon contributions to hadronic weak decays of mesons, are updated by extracting them from the data of D,rBMPP,r VP decays (P: pseudoscalar meson, V: vector meson). It is found that L₂ ranges from т.36 to т.60 in the decays from DMK¥? to D⁺MJ?⁺,r DMK¥^*?, while it is of order 10% with a positive sign in BMNK,r D?,r D^*?,r DA decays. Therefore, the effective parameter a₂ is process dependent in charm decay, whereas it stays fairly stable in B decay. This is in accordance with the picture that nonfactorizable soft gluon effects become stronger when the relative momentum of the decay particles becomes smaller. As for D,r BMVV decays, the presence of nonfactorizable terms in general prevents a possible definition of effective a₁ and a₂. This is reinforced by the observation of a large longitudinal polarization fraction in BMNK^* decay, implying nonfactorizable effects contributing differently to S-, Pand D-wave amplitudes. We found that A^nf₁/A₁>0> A^nf₂/A₂,r V^nf/V (nf standing for nonfactorization) for BMNK^* decay and 0>A^nf₁/A₁>A^nf₂/A₂,r V^nf/V for DMK¥^*A decay. A measurement of longitudinally and transversely polarized decay rates &_L and &_T in colorsuppressed decay modes B¥⁰MD^*0A⁰, D^*0P and D⁺M JA⁺ is urged.     

Skein Theory and Witten–Reshetikhin–Turaev Invariants of Links in Lens Spaces

We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of an arbitrary link in L(p,q) as a function of the level rф. They are given by \frac1?r\frac{1}{\sqrt{r}} times one of p Laurent polynomials evaluated at e^{\frac 2 pi 4pr}e^{\frac {2 \pi i} {4pr}}. The congruence class of r modulo p determines which polynomial is applicable. If p L 0 mod 4, the meridian of L(p,q) is non-trivial in the skein module but has trivial Witten-Reshetikhin-Turaev SU(2) invariants. On the other hand, we show that one may recover the element in the Kauffman bracket skein module of L(p,q) represented by a link from the collection of the WRT invariants at all levels if p is a prime or twice an odd prime. By a more delicate argument, this is also shown to be true for p=9.     

Ergodic Actions of Universal Quantum Groups on Operator Algebras

We construct ergodic actions of compact quantum groups on C^*-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1) an ergodic action of the compact quantum A_u(Q) on the type III_u Powers factor R_u for an appropriate positive Q ] GL(2, Â); (2) an ergodic action of the compact quantum group A_u(n) on the hyperfinite II₁ factor R; (3) an ergodic action of the compact quantum group A_u(Q) on the Cuntz algebra _boxclose_boxclose{\cal O}_n for each positive matrix Q ] GL(n, ³); (4) ergodic actions of compact quantum groups on their homogeneous spaces, as well as an example of a non-homogeneous classical space that admits an ergodic action of a compact quantum group.     

Local ζ-Function Techniques vs. Point-Splitting Procedure: A Few Rigorous Results

Some general properties of local ‘-function procedures to renormalize some quantities in D-dimensional (Euclidean) Quantum Field Theory in curved background are rigorously discussed for positive scalar operators mj + V(x) in general closed D-manifolds, and a few comments are given for nonclosed manifolds too. A general comparison is carried out with respect to the more known point-splitting procedure concerning the effective Lagrangian and the field fluctuations. It is proven that, for D>1, the local ‘-function and point-splitting approaches lead essentially to the same results apart from some differences in the subtraction procedure of the Hadamard divergences. It is found that the ‘ function procedure picks out a particular term w₀(w,y) in the Hadamard expansion. The presence of an untrivial kernel of the operator mj + V(x) may produce some differences between the two analyzed approaches. Finally, a formal identity concerning the field fluctuations, used by physicists, is discussed and proven within the local ‘-function approach. This is done also to reply to recent criticism against ‘ function techniques.     

Derivation of the Euler Equations¶from a Caricature of Coulomb Interaction

A caricature of collisionless plasma involving 2N particles of opposite charge is introduced. The N first particles are called "ions" and don't move. The N other particles are called "electrons". At each time, there is a one-to-one matching between electrons and ions and each pair is linked by a "spring" so that each electron oscillates with fixed frequency )^у. The essential point is that the matching between electrons and ions is updated at every discrete time n‰, n˸,1,2,..., so that the total potential energy of the system stays minimal. This leads to a non trivial interaction which turns out to be a caricature of Coulomb interaction. It is proven that, provided the N ions are equally spaced in a bounded domain D and ), ‰ and N^у tend to zero at appropriate rates, the electrons behave as the fluid parcels of an incompressible inviscid liquid moving inside D according to the Euler equations. Our proof relies on a result of P. Lax on the approximation of volume-preserving transformations by permutations.     

The Band Structure of the General Periodic¶ Schrödinger Operator with Point Interactions

The spectrum of Schrödinger operators H with periodic point potentials in dimensions d= 2, 3 is studied. In the general case of N points in the Wigner-Seitz cell it is proven that H has a band structure with at most a finite number of gaps (Bethe-Sommerfeld conjecture). It is also proven that in the case of a generic local point perturbation no singular continuous components are present; in the non-local case a fractal component like the Cantor set is exhibited, this component can either consist of a singular continuous or a dense point spectrum.     

Chiral Structure of Modular Invariants for Subfactors

In this paper we further analyze modular invariants for subfactors, in particular the structure of the chiral induced systems of M-M morphisms. The relative braiding between the chiral systems restricts to a proper braiding on their "ambichiral" intersection, and we show that the ambichiral braiding is non-degenerate if the original braiding of the N-N morphisms is. Moreover, in this case the dimensions of the irreducible representations of the chiral fusion rule algebras are given by the chiral branching coefficients which describe the ambichiral contribution in the irreducible decomposition of f-induced sectors. We show that modular invariants come along naturally with several non-negative integer valued matrix representations of the original N-N Verlinde fusion rule algebra, and we completely determine their decomposition into its characters. Finally the theory is illustrated by various examples, including the treatment of all SU(2)_k modular invariants.