Concept of field modes and the behavior of the magnetohydrodynamic field

A method for studying the behavior of fields by splitting their behavior into independent field modes is presented. The method is used to explore the characteristics of steady, two-dimensional, linearized magnetohydrodynamic fields with finite viscosity and resistivity and arbitrary orientation of the magnetic vector relative to the velocity vector.It is shown that in general boundary layers and wakes cease to exist in magnetohydrodynamics. Their place is taken by diffusing waves which, in reality, are the fields of a set of viscous-resistive sources, vortices, poles and currents whose field lines are strongly oriented along the characteristic wave directions. When the viscosity and resistivity are equal, these waves diffuse in a simple and independent way, but when these quantities are not equal, the diffusing waves generate a new kind of wake which is located, veil-like, in the fan-shaped region between the two wave directions. These wakes are fed from the differential diffusion of the primary waves. In the special case for which the resistivity is much greater than the viscosity, a new type of pseudo boundary layer is shown to exist in the velocity field. When the viscosity is much greater than the resistivity, this pseudo boundary layer occurs in the magnetic field

The Transient Behavior of Nonlinear Systems

It is shown that the classical perturbation procedure for treating nonlinear systems leads to solutions expressed as Fourier-like series with slowly varying coefficients. These slowly varying coefficients contain the information about the long term behavior of the system. Inconsistently, the classical perturbation procedure expresses these coefficients as power series, a mode of expression which has notoriously poor long term validity. An operational procedure is presented for treating oscillations having slowly variable amplitudes and frequencies. An extension of the usual impedance concepts is presented for expressing the frequency characteristics of both linear and nonlinear elements when oscillations with many frequencies are present simultaneously and when these oscillations vary in both frequency and amplitude. From these methods, a perturbation procedure is devised which permits the behavior of systems to be computed with any order of accuracy, using only the algebraic processes which are characteristic of operational procedures. This procedure avoids expressing its results in terms of the local time. Instead, it expresses them in terms of the fundamental characteristics of the oscillations which axe present. As a consequence, the final solutions have the much desired long term validity and they may be used to obtain asymptotic estimates of the behavior of the system. The method is able to treat systems containing nonlinear perturbing elements and elements which we have described as moderately nonlinear. By means of examples it is shown that it is a straightforward process to treat systems to second order accuracy. This level of accuracy covers a large number of the intercoupling effects that characterize the more sophisticated nonlinear phenomena

Factoring and Fourier Transformation with a Mach-Zehnder Interferometer

The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.Comment: 5 pages, 2 postscript figures; to appear in Phys.Rev.A, Nov. 1997; Figures contained only in replaced versio

Bell inequality and the locality loophole: Active versus passive switches

All experimental tests of the violation of Bell's inequality suffer from some loopholes. We show that the locality loophole is not independent of the detection loophole: in experiments using low efficient detectors, the locality loophole can be closed equivalently using active or passive switches.Comment: 6 pages, 1 figur

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure

Strict detector-efficiency bounds for n-site Clauser-Horne inequalities

An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented, for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the efficiency is greater than n/(2n-1). Thus, for a two-site two-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than 2/3. Secondly, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds 1/2.Comment: revtex, 5 pages, 1 figure (typesetting changes only

Bell inequality, Bell states and maximally entangled states for n qubits

First, we present a Bell type inequality for n qubits, assuming that m out of the n qubits are independent. Quantum mechanics violates this inequality by a ratio that increases exponentially with m. Hence an experiment on n qubits violating of this inequality sets a lower bound on the number m of entangled qubits. Next, we propose a definition of maximally entangled states of n qubits. For this purpose we study 5 different criteria. Four of these criteria are found compatible. For any number n of qubits, they determine an orthogonal basis consisting of maximally entangled states generalizing the Bell states.Comment: 8 pages, no figur

Interview with Francis H. Clauser

An interview in March 1983 with Francis H. Clauser, Clark B. Millikan Professor of Engineering, emeritus, and chairman of the Division of Engineering and Applied Science from 1969 to 1974. He recalls his arrival at Caltech in 1969 to head the engineering division; discusses the broadening of Caltech’s engineering option during the 1960s, including a shift toward fundamental research and an increase in the size of the faculty and the graduate program, enabled in part by a generous Ford Foundation grant. Comments on the current state of the division, with numerous retirements coming up and the opportunity for new hires. Recalls the establishment of the Environmental Quality Laboratory and the applied physics option. Discusses the development of computer science at Caltech and his efforts to build up communications science by recruiting John Pierce from Bell Labs. Comments on Caltech’s contributions to earthquake engineering. He concludes the interview by discussing his initiation of the Sherman Fairchild Distinguished Scholars Program

Characteristic modes and fundamental singularities of partial differential equations

Systems of linear partial differential equations with constant coefficients, like their ordinary differential equation counterparts, can be characterized by the properties of the matrices that form the coefficients of the differential operators. The question arises: Do the matrix operators that result from partial differential equations possess eigenvalues and eigensolutions in the same way that ordinary differential matrix operators do? The answer to this question is explored in some detail using as an example the linearized flow of a viscous fluid. It is shown that eigenfactors do exist for these equations, and that, of necessity, these involve hypercomplex algebra. This fact introduces significant new features to the problem. It is shown that eigenmodes exist and that each of these has its distinctive fundamental singularity. The fluid mechanical significance of these is examined in some detail. In addition, a representative group of other partial differential equations is examined and their eigenmodes and fundamental singularities are determined. It is shown that a number of basic differences exist between the eigenfunction theory for ordinary and for partial differential equations

Multi-Prover Commitments Against Non-Signaling Attacks

We reconsider the concept of multi-prover commitments, as introduced in the late eighties in the seminal work by Ben-Or et al. As was recently shown by Cr\'{e}peau et al., the security of known two-prover commitment schemes not only relies on the explicit assumption that the provers cannot communicate, but also depends on their information processing capabilities. For instance, there exist schemes that are secure against classical provers but insecure if the provers have quantum information processing capabilities, and there are schemes that resist such quantum attacks but become insecure when considering general so-called non-signaling provers, which are restricted solely by the requirement that no communication takes place. This poses the natural question whether there exists a two-prover commitment scheme that is secure under the sole assumption that no communication takes place; no such scheme is known. In this work, we give strong evidence for a negative answer: we show that any single-round two-prover commitment scheme can be broken by a non-signaling attack. Our negative result is as bad as it can get: for any candidate scheme that is (almost) perfectly hiding, there exists a strategy that allows the dishonest provers to open a commitment to an arbitrary bit (almost) as successfully as the honest provers can open an honestly prepared commitment, i.e., with probability (almost) 1 in case of a perfectly sound scheme. In the case of multi-round schemes, our impossibility result is restricted to perfectly hiding schemes. On the positive side, we show that the impossibility result can be circumvented by considering three provers instead: there exists a three-prover commitment scheme that is secure against arbitrary non-signaling attacks