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.     

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.     

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.     

Discontinuities of the Integrated Density of States for Random Operators on Delone Sets

Despite all the analogies with usual random models, tight binding operators for quasicrystals exhibit a feature that clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is identified as a local effect, due to the occurrence of eigenfunctions with bounded support.Research partly supported by the DFG in the priority program Quasicrystals     

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.     

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.     

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.     

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.     

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.     

Wave-function reconstruction in a graded semiconductor superlattice

We reconstruct a test wave function in a strongly coupled, graded well-width superlattice by resolving the spatial extension of the interband polarisation and deducing the wave function employing non-linear optical spectroscopy. The graded gap superlattice allows us to precisely control the distance between test and probe wave functions. By spatially tuning one wave function with respect to the other and recording the amplitude and the sign of the modulation of the spectrally resolved four-wave-mixing (FWM) signal with respect to delay, we are able to reconstruct the test wave function. Our numerical simulation of the third-order response of an inhomogeneously broadened system reproduces the experimental data in great detail. The wave function used for the modelling is computed by a one-dimensional transfer matrix model including electron–hole Coulomb interaction. Our experimental scheme inherently allows us to quantitatively distinguish between non-linear mechanisms leading to the FWM signal, namely phase-space filling and excitation-induced dephasing. PACS 78.47.+p; 71.35.Cc; 42.50.Md; 42.65.Re     

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     

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.     

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.     

Random Matrix Ensembles Associated to Compact Symmetric Spaces

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families of (unitary, orthogonal and symplectic) ensembles of Jacobi type. We discuss the universal and weakly universal features of the global and local correlations of the levels in the bulk and at the hard edge of the spectrum (i. e., at the central points ±1 on the unit circle). Previously known results are extended, and we find new simple formulas for the Bessel Kernels that describe the local correlations at a hard edge.This research has been supported in part by the FRG grant DMS–00–74028 from the NSF     

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     

Faux-boolean algebras,classical probability,and determinism

It is possible to define, for any quantum system, an algebra of definite-valued events—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain pseudo-Boolean algebra.     

A note on a paper by Atkin and Bastin

The paper A Homological Foundation for Scale Problems in Physics (Atkin & Bastin, 1970) is criticised on account of several inconsistencies in the argument. Possible applications of the general ideas used are then discussed in the context of a quantum logic type of framework.     

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.     

A Note on Symmetries and Generalized W∞ Algebra of the Modified KP Equation

Some remarks on the paper Symmetries and generalized W algebra of the modified KP equation (S. Y. Lou and G. J. Ni, Lett. Math. Phys. 34 (1995), 327–331) are given. It is pointed out that if we consider the inverse operator of a differential operator to be a linear operator, the vector fields nv(f) defined in the above Letter are not certain to be symmetries of the modified KP equation under consideration.     

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.