Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ∂/∂λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.     

Lower Bounds for Eigenvalues of the Stokes Operator

In this paper, we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes operator. We check and prove this condition for four nonconforming methods and one conforming method. Hence they produce eigenvalues which are smaller than their exact counterparts.     

Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.     

On the Number of Negative Eigenvalues of a One-Dimensional Schrödinger Operator with Point Interactions

An effective algorithm is provided for determining the number of negative eigenvalues of a one-dimensional Schrödinger operator with point interactions in terms of the intensities and the distances between the interactions.     

A Spin-Shift Operator of the Multi-particle Ruijsenaars–Schneider Hamiltonian

We obtain a spin-shift operator for the multi-particle trigonometric Ruijsenaars–Schneider Hamiltonian. This result is a generalization of the argument in Phys. Lett. B 375 (1996), 89–97, where the integrability of the one-particle Ruijsenaars–Schneider system is shown by using the existence of a spin-shift operator.     

Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

By applying the Fourier slice theorem, S_θ(λ) =∫_{-\infty }^{\infty }P_θ(t)e^-iλt=F(λcosθ,λsinθ), where P_θ(t) is a projection of f( x,p) =∫∫_{-\infty}^{\infty }F( u,v) e^i(ux+vp)ldudv along lines of constant, to the Wigner operator we are naturally led to projection operator (pure state), which results in a new complete epresentation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.     

The Constants in the Central Limit Theorem for the One-Dimensional Edwards Model

The Edwards model in one dimension is a transformed path measure for one-dimensional Brownian motion discouraging self-intersections. We study the constants appearing in the central limit theorem (CLT) for the endpoint of the path (which represent the mean and the variance) and the exponential rate of the normalizing constant. The same constants appear in the weak-interaction limit of the one-dimensional Domb–Joyce model. The Domb–Joyce model is the discrete analogue of the Edwards model based on simple random walk, where each self-intersection of the random walk path recieves a penalty e ^–2. We prove that the variance is strictly smaller than 1, which shows that the weak interaction limits of the variances in both CLTs are singular. The proofs are based on bounds for the eigenvalues of a certain one-parameter family of Sturm–Liouville differential operators, obtained by using monotonicity of the zeros of the eigen-functions in combination with computer plots.     

On the Essential Spectrum of a Class of Singular Matrix Differential Operators. I: Quasiregularity Conditions and Essential Self-adjointness

The essential spectrum of singular matrix differential operator determined by the operator matrix

Spectral Properties and Identities for the Polar Operator with Nonsmooth Periodic Density

Spectral properties of the polar operator depending on the smoothness of the periodic coefficient are studied. The width of the far gaps in the Bloch spectrum is shown to grow for piecewise continuous coefficients, to be asymptotically constant if the coefficient derivative is piecewise continuous, and to decrease in the more smooth cases. The high energy asymptotics of the Lyapunov function, of the quasimomentum and of effective masses are obtained. The spectral identities for the corresponding classical string equation are derived.     

Atomic,electronic, and vibronic structure of semiconductor surfaces

A brief review on recent progress in the theory of electronic, structural, and vibronic properties of semiconductor surfaces is presented with particular emphasis on the empirical and selfconsistent scattering theoretical method for semiinfinite systems. The current knowledge of the Si(001) (2×1) surface is discussed in detail. The Ge(001) (2×1) surface, as well as, the clean and the Ge-covered GaAs(110) surfaces are addressed, in addition. In the discussion of the results it is shown, that the scattering theoretical method is an extremely versatile tool for calculating electronic surface properties unambiguously with high spectral resolution concerning energy, wavevector, layer-index and orbital type. Currently used approaches for calculating the total energy, Hellmann-Feynman forces and optimal structure models are summarized. Using the total energy as a starting point, the calculation of atomic force constants and surface phonon spectra is exemplified.     

On the Persistence of Particles

This paper is about the metaphysical debate whether objects persist over time by the selfsame object existing at different times (nowadays called endurance by metaphysicians), or by different temporal parts, or stages, existing at different times (called perdurance). I aim to illuminate the debate by using some elementary kinematics and real analysis: resources which metaphysicians have, surprisingly, not availed themselves of. There are two main results, which are of interest to both endurantists and perdurantists. (1) I describe a precise formal equivalence between the way that the two metaphysical positions represent the motion of the objects of classical mechanics (both point-particles and continua). (2) I make precise, and prove a result about, the idea that the persistence of objects moving in a void is to be analysed in terms of tracking the continuous curves in spacetime that connect points occupied by matter. The result is entirely elementary: it is a corollary of the Heine–Borel theorem.Dedicated to the memory of Jim Cushing, an amazing mind and a wonderful man.     

Laser photoelectron microspectroscopy for imaging impurity ions,color centers,and small-size irregularities in dielectric media

New photoelectron microscopy application fields are considered for imaging the arrangement of color centers, small-size defects, and impurity ions in dielectric matrices. The techniques proposed are based on the first experimental results obtained in studying the possibilities of observing stepwise laser photoelectric effect in ZrO₂:Nd³⁺, where photoelectron emission results from the stepwise absorption of light by the impurity ions Nd³⁺. In that case, the electrons being emitted originate in immediate proximity to the impurity ions, which offers possibilities to image the above structures by photoelectron microscopy techniques.     

Steps Towards the Axiomatic Foundations of the Relativistic Quantum Field Theory: Spin-Statistics, Commutation Relations, and CPT Theorems

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed form the notion of basic field and system of basic fields. In comparison with others formulations, in our realistic approach fields are regarded as real things with symmetry properties. Finally, the general structure is contrasted with other formulations.     

The Nondynamical r-Matrix Structure of the Elliptic Calogero–Moser Model

In this Letter, we construct a new Lax operator for the elliptic Calogero–Moser model with N=2. The nondynamical r-matrix structure of this Lax operator is also studied. The relation between our Lax operator and the Lax operator given by Krichever is also obtained.     

Ion beam mixing and sputtering of Kr-irradiated TiN films measured with RBS,RNRA, and PIXE

Thin titanium nitride films of 10–300 nm thickness were irradiated with ⁸⁴Kr ions of 80–700 keV energy and fluences ranging from 10¹⁶ cm² to 2×10¹⁷ cm². Sputter yields (Y=0.4–1.0) and mixing rates (k=0.05–0.5 nm⁴) were determined using the depth profiling methods RBS, RNRA, and PIXE. While the sputter yields agree well with the modified Sigmund theory, the energy dependence of the mixing rates cannot be explained by standard models.     

Determinants,Grassmanniannians and Elliptic Boundary Problems for the Dirac Operator

We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type.     

Simultaneous formation of contacts and diffusion barriers for VLSI by rapid thermal silicidation of TiW

The formation of (Ti_xW_1–x)Si₂/(Ti_xW_1–x)N, by rapid thermal processing of Ti_xW_1–x on Si in an N₂ ambient is investigated. An activation energy of 1.7 eV is obtained for silicide formation. A distinct snow-ploughing of As atoms is observed during silicide formation whereas the interfacial B concentration decreases with increasing silicide formation temperature. The diffusion barrier properties of the (Ti_xW_1–x)Si₂/(Ti_xWi_1–x)N stack in contact with Al is investigated upon post-metal annealing. No interaction between the layers is found for temperatures as high as 475°C after 60 min. The improved thermal stability of the (Ti_xW_1–x)N layer in contact with Al is attributed to nitrogen blocking of the grain boundaries.     

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales. A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.     

Eigenvalues and eigenfunctions of the Fokker-Planck equation for the extremely underdamped Brownian motion in a double-well potential

The eigenvalues and eigenfunctions of the Fokker-Planck equation describing the extremely underdamped Brownian motion in a symmetric double-well potential are investigated. By transforming the Fokker-Planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate, a differential equation depending only on energy is derived. For finite temperatures this equation is solved by numerical integration, whereas in the weak-noise limit an analytic result for the lowest nonzero eigenvalue is obtained. Furthermore, by using a boundary-layer theory near the critical trajectory, the correction term to the zero-friction-limit result is found.