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.     

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.     

On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertzs experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertzs experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertzs crucial experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtzs electrodynamics did not contradict any of Hertzs experimental observations of transverse components as Maxwells theory predicted. Moreover, as we now know from recently published Hertzs dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertzs experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtzs theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.     

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.     

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.     

Laser action below threshold inversion due to coherent population trapping

The possibility of lasing without inversion on the 1079.8 nm line of a HeNe laser is investigated. It is shown that a modified double- scheme can be realized by use of the 877.9 nm line for introducing Zeeman coherence. It is shown experimentally that Zeeman coherence can enforce laser action, even if the inversion is below threshold. A different choice of the polarization of the driving beam can result in suppression of laser action above threshold. The underlying mechanisms are examined. On the 611.8 nm line, laser action below threshold inversion is obtained with the driving beam tuned to 824.9 nm (up-conversion).     

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.     

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).     

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.     

Gravity as Archimedes’ Thrust and a Bifurcation in that Theory

Eulers interpretation of Newtons gravity (NG) as Archimedes thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Eulers, is recalled and compared with the latter. None of these two gravitational ethers can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newtons second law. The observational status for the theory with the older version of the correspondence is summarized.     

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.     

Ritz,Einstein, and the Emission Hypothesis

Just as Albert Einsteins special theory of relativity was gaining acceptance around 1908, the young Swiss physicist Walter Ritz advanced a competing though preliminary emission theory that sought to explain the phenomena of electrodynamics on the assumption that the speed of light depends on the motion of its source. I survey Ritzs unfinished work in this area and review the reasons why Einstein and other physicists rejected Ritzs and other emission theories. Since Ritzs emission theory attracted renewed attention in the 1960s, I discuss how the earlier observational evidence was misconstrued as telling against it more conclusively than actually was the case. Finally, I contrast the role played by evidence against Ritzs theory with other factors that led to the early rejection of his approach.     

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     

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.     

Parametric dependence of the properties of pulsed-laser-deposited diamond-like carbon films

The properties of Pulsed-Laser-Deposited Diamond-Like Carbon (PLD DLC) films are studied as functions of the power density and the wavelength of the laser beam, and the incident angle of the beam relative to the normal of the target surface. All the films have a similar structure consisting of graphite particulates embedded in a continuous matrix, so the macroscopic performance of the films is determined by the overall contributions of the particulates and the matrix. The use of higher, shorter, or larger leads to an enhancement of the diamond-like characteristics and a simultaneous increase of the particulate density. These two effects give opposite contributions to the electrical conductivity _R, leading to the following results. (i) _R drops with increasing in the low range (region I) due to the stronger diamond-like nature of the matrix, but increases sharply after has exceeded a threshold _min as a result of the rapid increase in particulate density. (ii) In region I, the use of shorter or larger leads to a more diamond-like matrix, and this overwhelms the degradation effect caused by the slight increase in particulate density. The samples thus become more insulating. In the high region (region II), however, the use of shorter or larger gives rise to higher particulate density, thereby increasing the electrical conductivity.     

The Historical Roots of ‘‘Foundations of Quantum Physics’’ as a Field of Research (1950–1970)

The rising interest, in the late 20th century, in the foundations of quantum physics, a subject in which Franco Selleri has excelled, has suggested the fair question: how did it become so? The current answer says that experiments have allowed to bring into the laboratories some previous gedanken experiments, beginning with those about EPR and related to Bells inequalities. I want to explore an alternative view, by which there would have been, before Bells inequalities experimental tests, a change in the views shared by physicists concerning the intellectual status of that issue. I will take three cases which will serve as the threads of our story: the connections between Bohms causal interpretation and Bells inequalities; Wigners ideas on the measurement problem; and finally Everetts relative states formulation. In the end, I will discuss how those threads were gathered together by creating foundations of quantum physics as a field of research.