Stochastic Ornstein–Uhlenbeck Capacitors

We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is fed by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitors level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems Lévy-charged Ornstein–Uhlenbeck capacitors. Various random quantities associated with these systems are analyzed, including: the time-to- discharge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitors stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding standard Lévy-driven Ornstein–Uhlenbeck systems.     

Dual pairs of quantum spaces

We discuss the notion of metric dual pair corresponding to the algebraic condition in Alain Connes' definition of noncommutative Poincaré duality. We show that the DeRham complex of a metric dual pair is the homomorphic image of a skew tensor product, this leading to a natural definition of biconnections.     

Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an electron, interacting with massless, relativistic bosons, photons, is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of photons by the electron; but electron-positron pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed electron is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one–electron states with propagation estimates for the electron and the photons.Dedicated to Freeman Dyson on the occasion of his 80th birthdayWork partially supported by U.S. National Science Foundation grant DMS 01-00160.Acknowledgement. We thank V. Bach for his hospitality at the University of Mainz, where part of this work was done, and we are indebted to Gian Michele Graf for pointing out a serious gap in an earlier version of this paper. We also thank one of the referees for pointing out many typos and some small errors.     

Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’

The Inverse Scattering Transform is used to solve a class of nonlinear equations associated with the inverse problem for the one-dimensional Schrödinger equation with the energy-dependent potential V(k,x)=U(x)+kQ(x).Physique Mathématique et Théorique, Equipe de recherche associée au N.C.R.S. n⁰ 154.This work has been done as part of the program Recherche Coopérative sur Programme n⁰ 264: Etude interdisciplinaire des problèmes inverses.     

Perturbed periodic Hamiltonians: Essential Spectrum and exponential decay of eigenfunctions

Spectral properties of – +V(x), whereV(x) lies in a neighbourhood of the periodic case and describes various models of disorder, are studied. We prove the exponential decay of generalized eigenfunctions corresponding to energies in the resolvent set of the unperturbed periodic Hamiltonian, as well as the stability of the essential spectrum for the dislocation disorder in two dimensions.     

On the relation between weak and strong invariance of differential equations

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a strongly invariant equation exists, then all weakly invariant equations differ from it only by an arbitrary multiplicative factor. If no strongly invariant equation exists, then cohomology theory can be used to simplify the search for weakly invariant equations.     

Analysis of signal-to-noise ratio of the laser Doppler velocimeter

The signal-to-shot-noise ratio of the photocurrent of a laser Doppler anemometer is calculated as a function of the parameters which describe the system. It is found that the S/N is generally a growing function of receiver area, that few large particles are better than many small ones, and that generally the fringe or differential mode configuration is equal to, or better than, the reference beam mode.     

Mass splitting in relativistic quantum field theory

Null plane integrals of certain classes of tensor densities, conserved or non-conserved, may define symmetric operators on dense subspaces of the in and out states. These operators annihilate the vacuum and may satisfy a Lie algebra. In particular, the possibility that a finite number of null plane charges, which includes the Poincaré generators, close on an algebra whose irreducible representations contain particles with different masses is considered. The situation in which the Lie algebra is defined on a dense domain which is not from the in and out states is discussed. Some algebraic hypotheses other than that of a Lie algebra in the usual sense are briefly considered; in these cases there can be no mass splitting.Supported in part by the U.S.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel.     

The Wilson Loop Observables of Chern-Simons Theory on ℝ<Superscript>3</Superscript> in Axial Gauge

We define the Wilson loop observables (WLOs) for pure Chern-Simons models with base manifold M=³ rigorously as infinite dimensional oscillatory integrals by exploiting an axial gauge fixing and applying certain regularization techniques like loop-smearing and framing. The values of the WLOs can be computed explicitly. If the structure group G of the model considered is Abelian one obtains well-known linking number expressions for the WLOs. If G is Non-Abelian one obtains expressions which are similar but not identical to the state sum representations for the Homfly and Kauffman polynomials by Jones and Turaev.     

Sampling in holography of diffused objects or with diffused illumination

Differentiation between a diffused hologram and a specular hologram is determined by criteria of the wavelength and the relief of the object. In a hologram where the object beam is diffused (due to diffused object illumination, or because the object surface is reflecting diffusively), every part in the holographic plane contains information about the whole object, but from a different angle of view. In a specular hologram, the recording is somewhere between the image recording and the diffused holography. The latter part is contributed mainly by the edges of the object.This paper describes properties of sampled diffused holograms in terms of resolution,S/N (contrast), angle of view, power spectrum and the ability of determination of the object.Different sampling functions are compared and experimentally examined, while the total diffracting areas are preserved constant.It was found that when the sampling areas were distributed over the entire plane and the observation distance was preserved, the resolution, the angle of view and the ability of determination of the object was close to the unsampled hologram. At the same conditions theS/N and the power spectrum were reduced.It seems that these techniques of sampling may be applied for multiplexing, subtracting and correlating between two adjacent recordings.     

Crossing relations derived from (Extended) Relativity

Recently, Special Relativity has been straightforwardly extended to Superluminal inertial frames and faster-than-light objects. The Extended Relativity theory not only allowed building up a self-consistent classical theory of tachyons, but reveals itself useful also for the understanding of standard (subluminal) physics, i.e. of usual particles. In this paper, it is shown that Extended Relativity allows: (i) deriving the usual Crossing Relations of elementary particle (high-energy) physics; and (ii) deriving the CPT-covariance theorem as a particular case of G-covariance (i.e., covariance under the new group of Generalised Lorentz transformations, both subluminal and Superluminal).In this framework, the Analyticity postulate is unnecessary: it is better substituted by the G-covariance requirement.Moreover, new crossing-type relations are predicted on the basis of mere Extended Relativity. They may well serve as a test for relativistic covariance of force fields like strong interactions and, particularly, weak interactions, and possible new interaction fields (whicha priori are not relativistically covariant).     

The stress tensor in QED

The gauge-invariant point-splitting version of the energy-momentum tensor in QED is discussed with respect to Poincaré identities. In one-loop approximation an anomaly in the conservation law has been found for the triangle graph.This is part of the author's thesis, Tubingen 1974.     

Surface topology investigation for ancient coinage assessment using optical interferometry

In order to demonstrate the capabilities of white-light interferometry depth profiling (WLI-DP) for ancient coinage assessment, we investigated a series of notorious 1786 gold coins, bearing Louis XVIs horned effigy, and allegedly minted in Strasbourg. Scanning electron microscopy as well as WLI-DP observations unambiguously indicate that both previously differentiated single- and double-horned varieties originated from a unique minting tool. Moreover, from topological measurements, we infer that single-horned coins, rather than wearing out into double-horned coins, proceeded from the latter variety during minting by progressive failure of an already altered die. Whereas present observations do not exclude initial forgery, they suggest that protrusions resulted from progressive incidental in-service die deterioration. PACS 81.70.Fy; 07.60.Ly; 61.16.Bg; 81.40.Pq     

Algebraic quantization

The different correspondences (or orderings) used in quantum mechanics and the associated deformations, are both seen from an algebraic viewpoint. The deformations which are compatible with the diagonal map (the ₀-deformations) are introduced and connected to the formal groups. A very straighforward example of a ₀-deformation (the multiplicative deformation) appears in the normal quantization of the harmonic oscillator.     

The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

One massless particle equals two Dirac singletons

The remarkable representations of the 3+2 de Sitter group, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di Di, Di Rac, and Rac Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, massless particle may be interpreted as a state of two free singletons — and vice versa. The term massless is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.     

Ultrageneralised complex analysis

The zero rest mass Euclidean Dirac equations in 2 (4) dimensions may be regarded as square roots of the second order harmonic equation, and give rise to the crucial integral theorem and integral formula of complex (quaternionic) analysis. Recently discovered 2rth root equations for the 2rth order harmonic equations are here shown to give rise to a similar integral theorem and integral formula.     

Simple Realism and Canonically Conjugate Observables in Non-Relativistic Quantum Mechanics

In this paper we list some minimal requirements for a physically natural, straightforwardly realist interpretation of non-relativistic quantum mechanics. The goal is to characterize what one might call a simple realism of quantum systems, and of the observables associated with them.Simple realism as developed here is a generalized interpretation-scheme, one that abstracts important shared features of Einsteinian naive realism, the so-called modal interpretations, and the orthodox interpretation itself. Some such schemes run afoul of the classic no-go theorems, while others do not. The role of non-commuting observables plays a major role in this success or failure. In particular, we show that if a simple-realist interpretation attributes simultaneously definite values to canonically conjugate observables, then it necessarily falls prey to Kochen-Specker contradictions.This exercise provides some insight into why modal interpretations work, while more generally placing limits on the scope of simple realism itself. In particular, we find that within the framework of simple realism, the only consistent interpretation of the uncertainty relations is the orthodox one. What's more, we point out that similar conclusions are bound to hold for many other non-commuting observables as well.     

Current controlled negative resistance phenomenon in SbPbSe system

Thin film Al/Sb₂Pb₁Se₇/Al metal-glass-metal sandwiched structures prepared using thermal evaporation technique have been studied. The I–V measurements showed that the devices switched from high resistance OFF state to a low resistance ON state when a particular voltage appeared across it. The OFF state I–V characteristics showed non-ohmic behaviour while in the ON state the devices displayed purely linear characteristics. The switching voltage (V _th) was found to depend on film thickness and temperature of the device. A linear relation between V_th and temperature was observed.