Rational forms for twistings of enveloping algebras of simple Lie algebras

We give rational forms for twistings of classical enveloping algebras. We also remark a link with the generalized formalism of Gurevich, Manin, and Cartier.     

Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-type is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (positive and negative) sets of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation. This construction gives an embedding of the finite-dimensional small phase space of these models into the full space of flows of this hierarchy. One of flat coordinates in the small phase space turns out to be identical to the first negative time variable of the hierarchy, whereas the others belong to the positive flows.     

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.     

A formulation of linearised gravity

The formulation of linearised gravity in terms of the electric and magnetic gravitational fields is extended to take into account the presence of matter. The modes of radiation, the equations of motion and the potential in the static case are given. The relevant components of the superenergy tensor are calculated and a quantity named the superforce is introduced.     

Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

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.     

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.     

Nanoscale Characterization for the Classroom

This report describes the development of a semester course in nano-scale characterization. The interdisciplinary course is opened to both advanced undergraduate and graduate students with a standard undergraduate preparation in Materials Science, Chemistry, or Physics. The approach is formal rather than the typical research seminar and has a laboratory component.     

On Average Properties of Inhomogeneous Fluids in General Relativity: Dust Cosmologies

For general relativistic spacetimes filled with irrotational dust a generalized form of Friedmann's equations for an effective expansion factor a _D of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the backreaction effect of inhomogeneities on the average expansion of the model. A universal relation between backreaction and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to a _D ^-2, the expansion law governing a generic domain can be found. However, as the general equations show, backreaction acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.     

Modulated traveling waves in nonequilibrium systems: The ‘blinking state’

For the first time we give an explanation of the mechanism underlying the generation of modulated traveling wave states in nonequilibrium systems, frequently denoted as blinking state. The blinking state is generated by two nonlinearly interacting oscillatory modes with slightly different eigenfrequencies. Frequency locking between these modes generate spatial patterns experimentally known as confined states.     

Long-lived fluorescence probes for studying lipid dynamics: A review

A great many studies have focused on the heterogeneous packing of lipids in the bilayer matrix. However, less attention has been directed toward the temporal aspects of these lipid-lipid interactions. Studies of lipid packing fluctuations, or gel-fluid exchange, using fluorescence probe methodologies have been limited. This limitation arises from thesubmicrosecond time scale over which the fluctuations are expected to occur. Traditionally, dynamic studies of lipid bilayers have been restricted to the nanosecond time regime, and the submicrosecond time window has not been explored in any great depth by fluorescence methods, although persistent lipid dynamics has been evident. Probes with long fluorescence lifetimes (several hundred nanoseconds) have the potential to expand this important time window, providing information on gel-fluid exchange rates and insights into how important biological effectors such as proteins, cholesterol, and anesthetics affect or modulate these fluctuations. Using the long-lived fluorescence probe coronene, combined with time-resolved fluorescence methods geared toward microheterogeneity, we present a view of bilayer dynamics in an alternate time domain. Fluorescence probes are expected to inhabit an equilibrium between fluid and gel environments. Some probes remain in their respective environments throughout their excited-state lifetime, while others reside in surroundings that will change (i.e., melt). Long-lived fluorescence membrane probes can provide direct estimates of submicrosecond lipid fluctuation or melt rates. Simple Landau modeling leads to adistribution of melt rates and provides an attractive alternative to a simplercompartmental model where a unique lipid fluctuation of gel-fluid exchange rate is measured. Thedistribution model is probe independent (defined by thermodynamic quantities) and can be applied generally to the rotational motions of fluorescence probes embedded in the lipid bilayer.Abbreviations DMPC l--dimyristoylphosphatidylcholine - DPH 1,6-diphenyl-1,3,5-hexatriene - DPPC l--dipalmitoylphospha-tidylcholine - DSC differential scanning calorimetry - EA fluorescence emission anisotropy - LUV large unilamellar vesicles - SUV small unilamellar vesicles - T_c lipid phase transition temperature     

What is a hidden variable theory of quantum phenomena?

The purpose of this paper is to clarify the relationship between existing so-called hidden variable theories of quantum phenomena and some well-known proofs, such as those of von Neumann, Jauch and Piron, and Kochen and Specker, which purport to establish that no such theory is possible. The proof of Kochen and Specker, which is a stronger version of von Neumann's result, demonstrates the impossibility of embedding the algebraic structure of physical parameters of the quantum theory, represented by the self-adjoint Hubert space operators, into the commutative algebra of real-valued functions on a phase space of hidden states. This is a necessary condition for a hidden variable extension of the quantum theory in the usual sense of a statistical mechanical derivation of the statistical theorems of the quantum theory in the classical manner. No existing so-called hidden variable theory is a counter-example to von Neumann's proof. The early 1951 hidden variable theory of Bohm and the recent theory of Bohm and Bub are not in fact hidden variable theories in the usual sense of the term. Since the term hidden variable theory is justifiably used to denote the kind of theory rejected by von Neumann, Jauch and Piron, and Kochen and Specker, it is suggested that the term should not be used as a label for the theories considered by Bohm and other workers in this field. Such theories could be regarded as fundamentally compatible with the original Copenhagen interpretation of the quantum theory, as expressed by Bohr.Supported by the National Science Foundation.     

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.     

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.     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

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.     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

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.     

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).