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.     

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     

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.     

‘‘Extrinsic’’ and ‘‘Intrinsic’’ Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures

We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a meaningful (intrinsic) and a not meaningful (extrinsic) part. We are able to give an asymptotically tight separation of this form, with the intrinsic data quantified by the Holevo mutual information of a certain state ensemble associated to the POVM and the source, in a model that can be viewed as the asymptotic version of the convex decomposition of POVMs into extremal ones. This result is applied to a similar separation therorem for quantum instruments and quantum operations, in their Kraus form. Finally we comment on links to related subjects: we stress the difference between data and information (in particular by pointing out that information typically is strictly less than data), derive the Holevo bound from our main result, and look at its classical case: we show that this includes the solution to the problem of extrinsic/intrinsic data separation with a known source, then compare with the well–known notion of sufficient statistics. The result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics. An appendix collects several estimates for mixed state fidelity and trace norm distance, that seem to be new, in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity.     

On Shor’s Channel Extension and Constrained Channels

Several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity, are given. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for certain nontrivial classes of channels. After giving an algebraic formulation for Shors channel extension, its main asymptotic property is proved. It is then used to show that additivity for two constrained channels can be reduced to the same problem for unconstrained channels, and hence, global additivity for channels with arbitrary constraints is equivalent to additivity without constraints.     

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.     

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     

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.     

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.     

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.     

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.     

The Anisotropic Free Energy of the Solid-Liquid Phase Boundary in Al

We have performed large-scale molecular dynamics simulations of solid-liquid interfaces in aluminum, in order to calculate their interfacial stiffness and free energy. The anisotropy of these properties, though small, is key for determining the steady-state solutions for solidification in three dimensions. We find that the interfacial free energy, (), can be well represented by the form () = ₀(1 + cos 4, where measures the angle relative to the [100] interface, rotating about a [001] direction. We find values of ₀ = 120 ± 6 mJ/m² and = 1.3 ± 0.4%, in agreement with previous estimates and current experimental results.     

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.     

Der Einfluss der Beimengungen von Elementen der II. Gruppe auf die Thermolumineszenz von durch Kupfer und Silber aktivierten Natriumchlorid-kristallen

Zusammenfassung Der Artikel fa\t die Versuchsergebnisse über den Einflu\ von Beimengungen der II. Gruppe auf die spektrale Zusammensetzung der Thermolumineszenz von durch Kupfer oder Silber aktivierten Natriumchlorid-Kristallen zusammen. Ferner werden die VerÄnderungen angeführt, die in der spektralen Zusammensetzung dieser Lumineszenz als Folgeerscheinung einer Temperung der untersuchten Kristalle eintreten.

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Ich danke Dr. A. Bohun für das Interesse, das er dieser Arbeit entgegengebracht hat, und für die wertvollen Diskussionen, in denen er ihre Richtung beeinflu\te.     

‘Nonchiral’ Primary Superfields in the Add + 1/CFTd Correspondence

We consider some long multiplets describing bulk massive excitations of M-theory two-branes and IIB string three-branes which correspond to nonchiral primary operators of the boundary OSp(8/4) and SU(2,2/4) superconformal field theories. Examples of such multiplets are the radial modes on the branes, including up to spin 4 excitations, which may be then considered as prototypes of states which are not described by the K-K spectrum of the corresponding supergravity theories on Ad S4 × S7 and Ad S5 × S5, respectively.     

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.     

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.