Abstract: We study the fifth term in the asymptotic expansion of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with Dirichlet or Neumann boundary conditions.

Abstract: The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $ $ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $\sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.

Abstract: Locally narrow-band images can be modeled as two-dimensional (2D) spatial AM–FM signals with several applications in image texture analysis and computer vision. We formulate an image-demodulation problem and present a solution based on the multidimensional energy operator Φ(f) = ||∇f||2 − f∇2f. This nonlinear operator is a multidimensional extension of the one-dimensional (1D) energy-tracking operator Ψ(f) = (f′)2 − ff″, which has been found useful for demodulating 1D AM–FM and speech signals. We discuss some interesting properties of the multidimensional operator and develop a multidimensional energy-separation algorithm to estimate the amplitude envelope and instantaneous frequencies of 2D spatially varying AM–FM signals. Experiments are also presented on applying this 2D energy-demodulation algorithm to estimate the instantaneous amplitude contrast and spatial frequencies of image textures bandpass filtered by means of Gabor filters. The attractive features of the multidimensional energy operator and the 2D energy-separation algorithm are their simplicity, efficiency, and ability to track instantaneously varying spatial-modulation patterns.

Abstract: A diagonal equation for robot dynamics is developed by combining mass matrix factorization results with classical Lagrangian mechanics. Diagonalization implies that at each fixed time instant the equation at each joint is decoupled from all of the other joint equations. The equation involves two important variables: a vector of total joint rotational rates and a corresponding vector of working joint moments. The nonlinear Coriolis term depends on the joint angles and the rates. The total joint rates are related to the relative joint-angle rates by a linear spatial operator. The total rate at a given joint k reflects the total rotational velocity about the joint, and includes the combined effects from all the links between joint k and the base. Similarly, the working moments are related to the applied moments by the spatial operator . The working moment at a given joint is that part of the applied moment which does actual mechanical work. The diagonal equations are obtained by using the mass matrix factorization in the system Lagrangian. >

Abstract: Measurability and integrability in Hilbert spaces stochatic integrals in Hilbert spaces stochastic convolutions solutions of stochastic evolution equations - semigroups and evolution operator case, equations in rigged Hilbert spaces approximation of stochastic evolution equations examples in physics

Abstract: A many-particle operator that affects a transformation to the pseudospin basis in heavy nuclei is identified. Both mean-field and many-particle estimates demonstrate that in the helicity-transformed representation the nucleons move in a finite-depth nonlocal potential with a reduced spin-orbit strength. Because of the close relation between the helicity and chirality operations, the results suggest that the pseudospin symmetry in heavy nuclei yields to the chiral symmetry of massless hadrons in the high energy region.

Abstract: Semiclassical approximations for quantum time correlation functions are presented for both electronically adiabatic and nonadiabatic dynamics along with discussions of the operator ordering and the classical limit. With the combined use of the initial‐value representation of the semiclassical propagator, a discrete algorithm to evaluate the Jacobi matrices, semiclassical operator ordering rules, and the stationary‐phase filter technique, a practical algorithm is developed to calculate quantum time correlation functions. This approach holds considerable promise for simulating the quantum dynamics of realistic many‐body systems. Some simple illustrative examples are used to demonstrate the feasibility and accuracy of the algorithm.

Abstract: It is shown that there exist an infinite number of eigenvalues of the far field operator corresponding to the scattering of a time-harmonic plane wave by either an imperfectly conducting obstacle or an absorbing inhomogeneous medium. Regions in the complex plane are found where these eigenvalues must lie and, in the case of obstacle scattering, numerical examples are given showing how precise these regions are.

Abstract: A wave packet dynamical approach to the direct calculation of the rate constant of a chemical reaction is presented. Based on the position‐flux correlation function of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889 (1983)] a reaction rate operator is introduced, which can be viewed as the thermal analog of the energy‐dependent reaction probability operator [J. Chem. Phys. 99, 3411 (1993)]. It is shown that this reaction rate operator has in general only a small number of eigenstates with nonvanishing eigenvalues. These eigenstates can be interpreted as the vibrational ground state and the vibrationally excited states of the activated complex. The eigenstates and eigenvalues can efficiently be computed via an iterative (Lanczos) diagonalization scheme. The number of wave packet propagations required equals approximately the number of relevant states of the activated complex, it is considerably smaller as in previous approaches to the calculation of rate constants based on wave packet dynamics. The ne...

Abstract: A description of generalized resolvents for a densely defined Hermitian operatorA in a Krein space\(\mathcal{K}\) is given under explicit consideration of the number of negative squares of the inner product on the extending space and of the forms [A·,·], [A·,·],A being a selfadjoint extension ofA which corresponds to the generalized resolvent. New classesNkκ of analytic functions are introduced for this purpose. An application to a Sturm-Liouville operator with indefinite weight function is discussed.

Abstract: A current of the deformed Virasoro algebra is identified with the Zamolodchikov-Faddeev operator for the basic scalar particle in the XYZ model.

Abstract: Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage of the localization of quantum states into wave packets occupying small regions of classical phase space. Following and extending the original proposal of Percival, Alber and Steimle, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in computational space and time. Because of these gains, it is even possible to calculate an open quantum system trajectory when the corresponding isolated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum effects. The principles are illustrated by computations for the quantum Duffing oscillator and for second harmonic generation in quantum optics. Potential applications in atomic and molecular dynamics, quantum circuits and quantum computation are suggested.

Abstract: The phase space formulation of quantum statistical mechanics using the Feynman path centroid density offers an alternative perspective to the standard Wigner prescription for the classical‐like evaluation of equilibrium and/or dynamical quantities of statistical systems. The use of this formulation has been implicit in recent work on quantum rate theories, for example, in which the centroid density distribution replaces the classical Boltzmann distribution. In order to further understand the approximations involved in this and similar transcriptions, the present work elaborates and clarifies the issue of operator ordering in a rigorous centroid‐based formulation. In particular, through the use of the Weyl correspondence, a precise definition of the centroid symbol of operators and their products is presented. Though we fall short of finding the algebraic structure tantamount to that found in the Weyl symbols—of which the Wigner distribution is an example— the resulting expressions have internal consistenc...

Abstract: An eigenvalue-free region is determined for the far field operator corresponding to the scattering of time harmonic acoustic or electromagnetic waves by an inhomogeneous medium. In addition, a simp...

Abstract: We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]

Abstract: The cross sections for single and double photoionization of helium at energies from the threshold of double ionization to 280 eV are calculated by combining the previously developed hyperspherical close-coupling method with a discretization procedure for the continuum spectrum of ${\mathrm{He}}^{+}$. No pseudoresonances due to the discretization are found. Both the length and acceleration forms of the dipole operator are used, and the results hardly depend on these different gauges. The results are compared with previous theories and experiments.

Abstract: We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten.

Abstract: Demonstrates that although standard paraxial and wide-angle vector field propagation techniques lead to divergences for sufficiently small grid-point spacings and large refractive index differences, stability may be restored through either certain Pade approximates to the propagation operator or suitable boundary conditions. The authors also introduce a novel alternating directional implicit method applicable to less divergent discretizations of the vector wave equation. >

Abstract: An efBcient method developed for the calculation of quasiparticle corrections to densityfunctional-theory — local-density-approximation (DFT-LDA) band structures of diamond and zincblende materials is generalized for crystals with other cubic, hexagonal, tetragonal, and orthorhombic Bravais lattices. Local-field efFects are considered in the framework of a LDA-like approximation. The dynamical screening is treated by expanding the self-energy linearly in energy. The anisotropy of the inverse dielectric matrix is taken into account. The singularity of the Coulomb potential in the screened-exchange part of the electronic self-energy is treated using auxiliary functions of the appropriate symmetry. An application to the electronic quasiparticle band structure of wurtzite 2HSiC is presented within the approach of norm-conserving, nonlocal, fully separable pseudopotentials and a plane-wave expansion of the wave functions for the underlying DFT-LDA. Electronic-structure calculations for solids using density-functional theory (DFT) within the local-density approximation (LDA) are not capable of yielding reliable excitation energies. For semiconductors this fact is known as the so-called energy band gap problem. The correction to the Kohn-Sham eigenvalues giving the accurate quasiparticle (QP) energies of the crystal electrons may be obtained by first-order many-body perturbational theory, with respect to the difference between the exchange-correlation (XC) self-energy and the corresponding XC potential of the DFT-LDA. Thereby the self-energy is treated within the GTV approximation of Hedin. One of the crucial points in such calculations is the evaluation of the self-energy operator, which may be numerically very expensive, because of the required knowledge of the full inverse dielectric matrix of the system and the careful treatment of the singularity, due to the Coulomb potential entering the screenedexchange (SX) contribution to this operator. In order to decrease this remarkable numerical effort, one may follow the efBcient calculational scheme introduced by Cappellini et al. , 4 for semiconductors with diamond or zinc-blende structure. The local-field contributions to the screened Coulomb potential are described within a LDA-like treatment. The electron density governing the screening properties is replaced by state-averaged values of the local density. The dynamics of the screening is considered by a linear expansion of the self-energy operator around the Kohn-Sham eigenvalues. A substantial reduction of the computational effort arises from the use of a model dielectric function. This gives rise to an analytical representation of the static Coulomb-hole (COB) contribution to the self-energy. The Coulomb singularity in its SX part is treated according to the notion of Gygi

Abstract: Elements of the Mathematical Formulation of the Quantum Theory.- Performance Criteria: Detection, Information.- Direct Detection Processing.- Phase Operator.- Conclusion.

Abstract: In preceding papers we have shown how the analysis of the transfer matrix method in statistical mechanics permits us to get a very natural result for the splitting for the transfer matrix. The purpose of this note is to analyze the link between this result and previous results obtained by J.Sjostrand concerning the splitting between the two first eigenvalues of the Schrodinger operator. We present here improved results and analyze as a byproduct the convergence in the Trotter-Kato formula in a particular (non abstract but relatively general) case. As is known this is strongly related with the Feynman-Kac formula.

Abstract: We evaluate several approximations for the self-energy operator and dielectric function of systems of interacting electrons using a two-dimensional Hubbard cluster for which the self-energy, dielectric function, and one-particle Green's function may be calculated exactly. The results show the GW approximation (in the form in which it is commonly used in ab initio calculations for real materials) to be relatively successful in establishing the main features of the spectrum, even when the electron-electron interaction is not weak. It is also clear that improving the G andW used in this approximation without including vertex corrections in the self-energy does not lead to major improvements.

Abstract: In this paper, we consider the following linear system of single input on a separable Hilbert space H: /spl phi//spl dot/(t)=A/spl phi/(t)+bu(t), where the operator A is the generator of a C/sub 0/-semigroup on R and the vector b is not necessarily in H (for the case of boundary controls). We assume that the operator A has compact resolvents, the spectrum of A is discrete and simple and the eigenvectors of A form a Riesz basis in H. We study the spectrum assignability of the system by bounded linear feedbacks of the form: u(t)= /sub H/ for h/spl isin/H. Under some conditions on the distribution of the spectrum of A and the relative largeness of b we prove the necessary and sufficient condition of Sun (1981) for a given set of points to be assigned to the system by a bounded linear feedback. Given an assignable spectrum set we present explicitly the linear feedback law which realizes it and prove that the eigenvectors of the resulted feedback system form also a Riesz basis in H.

Abstract: This paper analyzes the n-fold composition of a certain non-linear integral operator acting on a class of functions on [0,1 ]. The attracting orbit is identified and various properties of convergence to this orbit are derived. The results imply that the space-time scaling limit of a certain infinite system of interacting diffusions has universal behavior independent of model parameters.

Abstract: The main theorem establishes the existence of a positive decaying solution u ∈ D 0 1,p (Rn) of a quasilinear elliptic problem involving the p-Laplacian operator and the critical Sobolev exponent pN/(N - p), 1