A theorem concerning the positive metric

It is proved that if then-point correlation functions of a system vanish for alln>N then they vanish for alln>2. The theorem is valid for a wide variety of formalisms and an explicit proof is given for a Bose system with the canonical commutation relations; a proof is sketched out for a relativistic field theory of the Wightman type. The essential property used in the proof is the positive definite metric.     

Loop dynamics for gauge theories: A numerical algorithm

The loop equations defining the lattice U(N) gauge theory are recalled and a formal solution is presented (for N = 1 and N → ∞). Wilson's expectation function W(C) for a loop C is expressed as a matrix element of a resolvent in the space of all the loops between C and 0 (no loop). It is shown that such a solution provides a new numerical algorithm to compute physical quantities. This is based on a Ulam-von Neumann type of method for computing inverse matrix elements by introducing importance sampling for the paths in the space of the matrix indices, which in this case are the loops. As a result W(C) is obtained by summing over important paths in the loop space connecting C to 0. A Monte Carlo program is presented, for the N → ∞ case, where a very simple form for the importance sampling is introduced so that the computer time for each step in the construction of the path is minimized. The rates for successful paths (i.e. path C → 0 within a given finite number of steps) are computed for D = 2 and D = 4. Both rates and computer time involved encourage us to attempt a large scale calculation. Here the numerical studies of the convergence and of the fluctuations are presented only for D = 2. Convergence is rather fast, but specially in the weak-coupling region rare and large fluctuations appear thus suggesting that a better tuning for the importance sampling is needed.     

FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions

An effective numerical method based on the finite-difference time-domain scheme for computing the off-plane band structure of a two-dimensional photonic crystal is presented. The method is an order N method, and requires only a two-dimensional discretization mesh for a given off-plane wave number k_z although the off-plane propagation is a three-dimensional problem. The computation time and memory required is thus reduced significantly. The present method can be used for any type of inclusions and no additional effort is needed for metallic inclusions. The off-plane band structures of a square lattice of metallic rods in the air are studied, and a complete bandgap for some nonzero off-plane wave number k_z is found.     

Linear Amplifier Breakdown and Concentration Properties of a Gaussian Field Given that its <Emphasis Type="BoldItalic">L</Emphasis><Superscript>2</Superscript>-Norm is Large

In the context of linear amplification for systems driven by the square of a Gaussian noise, we investigate the realizations of a Gaussian field in the limit where its L ²-norm is large. Concentration onto the eigenspace associated with the largest eigenvalue of the covariance of the field is proved. When the covariance is trace class, the concentration is in probability for the L ²-norm. A stronger concentration, in mean for the sup-norm, is proved for a smaller class of Gaussian fields, and an example of a field belonging to that class is given. A possible connection with Bose-Einstein condensation is briefly discussed.     

On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

Short- and long-range screening of optical phase singularities and C points

Screening of signed (charged) singularities-phase vortices in scalar fields, C points in vector fields, is discussed for paraxial optical fields with short- and long-range correlations. A circular region of radius R is assumed. Short-range screening is exemplified by a Gaussian field correlator, long-range screening by a J₀ Bessel function. The short-range screening length is obtained analytically; this is found to be in substantial agreement with recent experiments. For long-range screening, an accurate asymptotic formula suitable for quantitative comparison with data (numerical or laboratory) is derived for the variance of the net charge. A J₀ correlation function is not attainable in practice, but it is shown how to generate a pseudo-long-range optical field whose correlation function closely approximates this form; screening in such a field is well described by our theoretical results for J₀. The charge variance can be measured by three different methods: by counting positive and negative singularities inside the region of interest, by counting signed zero crossings on the perimeter of this region; or by measuring phase derivatives along the perimeter. For the first method, the charge variance is calculated by integration over the charge correlation function, for the second (third) by integration over the zero crossing (phase derivative) correlation function. It is proven explicitly that, as expected, all three calculations yield the same result. It is also shown analytically that for short-range screening the zero crossings can be counted along a straight line whose length is 2πR, but that for long-range screening this useful simplification no longer holds; for this case another formula is given that is suitable for data correction. The effects of boundary smoothing are discussed, and a class of generalized exponential smoothing functions is introduced. Analytical (numerical) results are given for the large R limit of the charge variance for the short (long) range case. Finally, it is shown that for realizable optical fields, both for the short and pseudo-long-range cases, for sufficiently small R the charge variance grows as R², whereas for sufficiently large R it grows as R.     

Evaluation of the photoionization probability of H2+ by the trajectory semiclassical method

The trajectory-based method for calculating the probabilities of transitions in the quantum system developed in our previous works and tested for atoms is applied to calculating the photoionization probability for the simplest molecule – hydrogen molecular ion. In a weak field it is established a good agreement between our photoionization cross section and the data obtained by other theoretical methods for photon energy in the range from one-photon ionization threshold up to 25 a.u. Photoionization cross section in the range $25<\omega \le 100$ a.u. was calculated for the first time judging by the literature known to us. It is also confirmed that the trajectory method works in a wide range of the field magnitudes including superatomic values up to relativistic intensity.     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

A New Laser Photochemical Process for Isotope Enrichment

Selective laser excitation of a specific isotopic species to its lowest electronic singlet (S₁) and triplet (T₁) states respectively, then followed by a chemical reaction for isotope separation is examined theoretically. It is found that the direct excitation to T₁ state from ground state (S₀) is an unique excitation channel for obtaining a controllable chemical reaction and for achieving a high isotope separation factor. This is due to the following important facts: 1) Resonant energy transfer from a selectively excited triplet isotopic species to an unexcited species of the other isotope present in the mixture is missing (or is very small); 2) The lifetime of the T₁ state is normally longer than that of the S₁ state; 3) There is no intersystem crossing channel that exists for the deactivation of excited isotopic species from T₁ state.

Numerical calculation is performed for the chlorine isotope separation in a mixture of thiophosgene (0.5 torr) and diethoxyethylene (1.5 torr). The result indicates that the isotopic enrichment factor is at least 2.5 × 10³ times larger for selective T₁ excitation than that for S₁ excitation.     

Compact Mode Converter System for the Cold Test of Assembled Gyrotrons

A microwave system is described which allows testing of the quasi-optical mode converter in a gyrotron, which is completely assembled except for the attachment of the electron gun. Test results are presented for a TE_6,2,1 gyrotron, and a similar design for a TE_28,7,1 gyrotron is shown.     

Shooting algorithm and particle swarm optimization based Raman fiber amplifiers gain spectra design

An initial value determination method with a contraction factor for the counter-pumped Raman coupled equations is proposed. This method is used in conjunction with initial guess correction mechanism of Newton's method to construct a new efficient shooting algorithm for the solution of counter-pumped Raman coupled equations. The particle'swarm optimization is used to find the optimal wavelengths and powers for the pumps. By combining the new shooting algorithm and particle swarm optimization a powerful approach to the design of gain spectra for Raman fiber amplifiers is developed. Using this approach a counter-pumped broadband Raman fiber amplifier in C + L-band is designed and optimized. An average on-off gain of 9.3 dB for a bandwidth of 95 nm is obtained using only 4 pumps, with an in-band ripple level of ± 0.7 dB.     

On a new condition distinguishing Weyl and Lorentz space-times

The paper is concerned with the derivability of a Lorentz instead of only a Weyl manifold as space-time structure from postulates about free fall and light propagation. For this purpose it identifies a property distinguishing both kinds of space-times. The property is one of a particular metric of the conformal class of the Weyl manifold. viz. that in suitably chosen locally geodesic coordinates theg _i4 components,i=1, 2, 3 vanish along the time axis. Although seemingly somewhat hidden, one is led to this property in looking for a metric which can play a distinguished role. We demonstrate that for a Lorentzian manifold such a condition is always given; thus it is a necessary one. It is sufficient since for a Weyl space it has the consequence that the metric connection of the selectedg is projectively equivalent to the Weyl connection. Thus, if a Weyl space-time complies with it, it is a reducible one. The results of this paper lay the ground for deriving in a second step this condition from a simple, empirically testable postulate about free-fall worldlines and “radar” measurements by light signals.     

Ewald method for polytropic potentials in arbitrary dimensionality

The Ewald summation technique is generalized to power-law 1/| r | ^k potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and ‘marginal’ interactions are treated separately. The jellium model, as a particular case of a charge-neutral system, is discussed and the explicit forms of the Ewald sums for such a system are presented. A generalized form of the Ewald sums for a non-cubic (non-square) simulation cell for three- (two-) dimensional geometry is obtained and its possible field of application is discussed. A procedure for the optimization of the involved parameters in actual simulations is developed and an example of its application is presented.     

Theory of a waveguide laser

The role of diffusion of the components of the gas mixture is the generation mechanism of a waveguide CO₂ laser is analyzed. A method is proposed for reducing the multicomponent problem of linear diffusion with dissipation to a one-component problem. The superposition of relaxation modes for a cylindrical waveguide is considered. The diffusion contribution to the loss of electromagnetic energy is estimated for the case of the field hybrid mode EH₁₁ of a dielectric waveguide. The rapid increase in the loss for a SiO₂ waveguide tube and the observation of the filtration properties of the laser in conditions when the diffusion is taken into account are noted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 17–21, July, 1975.     

Analysis of the magnetic field, force, and torque for two-dimensional Halbach cylinders

The Halbach cylinder is a construction of permanent magnets used in applications such as nuclear magnetic resonance apparatus, accelerator magnets and magnetic cooling devices. In this paper the analytical expression for the magnetic vector potential, magnetic flux density and magnetic field for a two dimensional Halbach cylinder are derived. The remanent flux density of a Halbach magnet is characterized by the integer p. For a number of applications the force and torque between two concentric Halbach cylinders are important. These quantities are calculated and the force is shown to be zero except for the case where p for the inner magnet is one minus p for the outer magnet. Also the force is shown never to be balancing. The torque is shown to be zero unless the inner magnet p is equal to minus the outer magnet p. Thus there can never be a force and a torque in the same system.     

Freezing of nonequilibrium domain structures in a kinetic Ising model

We study the freezing of a disordered spin structure upon continuous cooling to absolute zero for a kinetic Ising spin chain with alternating weak and strong bonds. The kinetic equation for the spin pair correlation function is solved analytically in a continuum approximation. The exponent for the asymptotic dependence of the frozen kink density on a characteristic cooling time is found to bez ^–1, wherez is the equilibrium dynamic critical exponent, for a universality class including power-law and exponential cooling, and 1/2 for a logarithmic cooling program which exhibits threshold behavior.     

The FN solution of the time-dependent neutron transport equation for a sphere with forward scattering

The one-speed time-dependent and stationary neutron transport equation in spherical geometry with forward scattering is considered. A formal equivalence between the transport equations for a critical and for a decaying system is established. By considering the pseudo-slab problem the scaled transport equation is solved using the F_N method. Numerical values of radii for a critical and time-dependent systems are tabulated as a function of the scattering parameters and the fundamental decay constant. Some of the results are discussed and compared with others obtained using various methods. The results agree for four or five significant figures with the published results. It is shown that the F_N method yields good numerical results for the problem considered. Finally, a few remarks about the effect of the forward anisotropy on the radius is also given.     

Loss reduction of dielectric-coated metallic hollow waveguides for CO2 laser light transmission

A condition for reducing transmission loss of a dielectric-coated metallic hollow waveguide is shown theoretically when the inner metallic surface is not perfect. It is also shown that the transmission loss for CO₂ laser light is 10.6 μm wavelength is able to be estimated from an attenuation spectrum of a short waveguide. By fabricating a ZnSe coated Ag hollow waveguide of short length, we have shown that it has a lower loss than a Ge coated waveguide for CO₂ laser light.     

Molecular-weight scaling of coexistence curves for monodisperse polymer solutions

The available data for the polymer volume fraction along the coexistence curves for monodisperse solutions of polystyrene in methylcyclohexane are used to derive the exponent z ≈ 0.61 such that the “correct” order parameter is only a function of ?M^Z (M is the polymer's molecular weight while ? is the reduced temperature). It is shown that a knowledge of the “correct” order parameter is unnecessary for a determination of z which is expected to be universal, i.e. independent of the polymer-solvent system.