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.     

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.     

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.     

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.     

Gauge-invariant variations in the redshift and cosmic background radiation anisotropies

The gauge-invariance of the calculations determining anisotropics in the cosmic microwave background radiation (the Sachs-Wolfe effect) is re-examined. It is shown that the results obtained are gauge-invariant only if a physically-based definition of the surface of last scattering is implemented, in a context where perturbations of the surface of last scattering as well as of the space-time are taken into account. Any physical interpretation of the results based on their splitting into scalar, vector, and tensor parts, is unique only if non-local (unverifiable) conditions are imposed; locally, any such interpretation is non-unique. The physical meaning of the Sachs-Wolfe potentialB and associated redshift formula depends on implementing a very specific gauge, without a clear physical or geometric meaning; its implications do not extend to other, more usual, gauges.     

The ground state of the Bose gas

The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of factorisable off-diagonal long range order. The class of quasi free states is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these quasi free states to the interacting Bose gas are summarized.     

‘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.     

Quantum fog and the degradation of information by the gravitational field

In this paper we discuss how information transferred optically through a gravitational field is degraded as the quanta interact with the madium (vacuum state). We quantify information by means of Shannon's entropy, and consider information carriers that are quanta of some field. Next, we obtain the quantum noise (quantum fog) produced by the gravitational field and derive the appropriate channel capacity formula, which quantifies the maximum amount of information that can be transmitted per pulse, in the face of this noise. We show that the channel capacity formula vanishes if the source of information is a space-time singularity because a very intense noise is produced in the vicinity of the singularity. In other words, space-time singularities are hidden behind a very intense quantum fog and cannot be optically observed. A second consequence is that information is degraded as anisotropies (lumpiness) develop in the universe.     

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).     

Libraries from libraries: Generation and comparison of screening profiles

Summary A positional scanning tetrapeptide library was chemically modified through alkylation and/or reduction of the amide bonds, thus generating three new combinatorial libraries with physico-chemical properties very different from the parent peptide library (libraries from libraries). Specific results were obtained with each of these libraries upon screening in -opioid receptor binding and microdilution antimicrobial assays, illustrating the potential of the libraries from libraries concept for the efficient generation of a variety of chemically diverse combinatorial libraries.     

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.     

Eigenresonance states in the Kronig-Penney model

We investigate a sandwich of three layer systems with Dirac -functions in the Kronig-Penney model. The inner system ofN=5 atomic layers is enclosed by the two outer systems with different potential strength. The numberM of the atomic layers in the outer system is varied betweenM=9 and infinity, whereas the numberN of the inner layers is held fixed. We obtain the transmission coefficient for the finite system in the region of scattering energies (E>0). An alternating set of transmission gaps, transmission bands and bands of eigenresonance states is obtained. The normalizable eigenresonances occur (forM going to infinity), if a transmission band of the inner system overlaps a transmission gap of the outer systems. The reason for obtaining solutions of standing waves in the band of eigenresonances is the rapid change of the wave phase of a traveling wave, which occurs in a transmission band of the inner system.     

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     

Nanocomposite Mullite/Mullite Powders by Spray Pyrolysis

A mullite/mullite nanocomposite powder has been synthesized, composed of nanometer-size 3Al₂O₃·2SiO₂ (3/2) mullite precipitates within a matrix of the high alumina 2Al₂O₃·SiO₂ (2:1) mullite. Historically, the transition from the metastable high-alumina phase to the thermodynamically stable 3:2 phase of mullite has been thought to be a continuous process, involving a continuous solid solution between the two forms of mullite. In contradiction to this widely held view, our high resolution transmission electron microscopic characterization confirms that a first order phase transition between two distinct mullites occurs. The high degree of interface coherence between the precipitates and the matrix allows us to speculate that the mechanical properties of the matrix could be enhanced by a process similar to the precipitation hardening of metals.     

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.     

Rate equations and transient phenomena in semiconductor lasers

This contribution attempts to review certain resonance effects which occur in the dynamic behaviour of semiconductor lasers. To study these effects theoretically, a rate equation approach is used for single-mode operation in the region of lasing threshold.The two basic rate equations are given and their transient solutions discussed. The existence of two time constants in these equations, viz. the electron lifetime _e and the photon lifetime _e; gives rise to a characteristic resonance frequency in the GHz region. This resonance manifests itself in transient spiking effects, in quantum noise phenomena, and in high-frequency modulation experiments. In a modified form the resonance frequency may also be studied in lasers with external cavities and in double-diode configurations (or, equivalently, conventional devices with non-uniform excitation along the cavity length).In the latter two examples mentioned above, the resonance is excited by optical feedback of the laser radiation into the active medium via a lossy or insufficiently inverted region. In the spiking oscillations commonly observed at the commencement of laser operation, the initial population overshoot is the cause of the resonance. For the case of quantum noise it is the requirement that the photon and electron populations have integer values which supplies the driving force-a true quantum effect. High-frequency modulation experiments directly reveal the same resonance frequency where a strong maximum in modulation intensity occurs.A part of this work was reported at the Conference on Semiconductor Injection Lasers and their Applications, Cardiff, March 1972.     

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.     

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.     

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     

Nonequilibrium response of a disordered Ising chain

The relaxation behaviour of a model disordered system is studied. The model considered is a nearest neighbour Ising chain in which the bond strengths are distributed at random between the discrete values +J and -J with equal probability. The system is prepared in a given state and is allowed to relax to a new state of equilibrium. This approach to equilibrium is probed by means of an applied, weak, time-dependent magnetic field. The relevant physical quantity is a nonequilibrium susceptibility which is calculated exactly. A comparison between this, and the corresponding quantity for the pure chain, reveals certain distinctive features of the time-dependent properties of disordered systems.Deceased