Quantum Automata: An Overview

Quantum state machines are introduced.Amplitudes of computational paths, computational bases,superposition states, and evolution operators arediscussed. The main part of the paper develops a theoryof quantum automata and their slightly moregeneral versions, q-automata. Quantum languages and-quantum languages, 0 < 1, arestudied. A method is given for reducing the size of thestate space. Functions that can be realized as probabilitymaps for q-automata are characterized. Quantum gates arediscussed. A quantum pumping lemma is employed to showthat there are regular languages that are not -quantum, 0 < 1. The papercloses with a list of open problems.     

Quantum Pushdown Automata

Quantum automata are mathematical models for quantum computing. We analyze the existing quantum pushdown automata, propose a q quantum pushdown automata (qQPDA), and partially clarify their connections. We emphasize some advantages of our qQPDA over others. We demonstrate the equivalence between qQPDA and another QPDA. We indicate that qQPDA are at least as powerful as the QPDA of Moore and Crutchfield with accepting words by empty stack. We introduce the quantum languages accepted by qQPDA and prove that every -q quantum context-free language is also an -q quantum context-free language for any (0, 1) and (0, 1).     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

The influence of a surface on Ising and conjugate model spin correlations atT=T c

We calculate rigorously the two-point correlation function in the 2-d Ising model on a quasi-cylindrical lattice at the critical temperatureT _c .The scaling predictions for the surface critical exponents = 5/8, = 1 are confirmed and the change from surface to bulk behavior is studied. By a correspondence relation the results are mapped to the conjugate model, a subcase of the 8-vertex model. We find in this model = 5/4, = 2.     

Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

The η N interaction cross section near the S11N*(1535) resonance

Calculations are presented for the integral cross-sections ofN N, N N incorporating the one-particle intermediate state, theS₁₁N * resonance; cross-sections are given for kinetic energies of the meson from 0 to 200 MeV for various values of the width of the resonance. The calculated cross-sections agree with experiment for r 160 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 119–122, July, 1973.We are indebted to our colleagueat the Institute G. N. Radutskom forvaluable advice and discussion on this paper.     

Yet another formulation of the Dirac equation

The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors and *_µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain .     

Metastates in Disordered Mean-Field Models II: The Superstates

We continue to investigate the size dependence of disordered mean-field models with finite local spin space in more detail, illustrating the concept of superstates as recently proposed by Bovier and Gayrard. We discuss various notions of convergence for the behavior of the paths (t_[tN]()) _{t(0, 1]} in the thermodynamic limit N. Here _n () is the Gibbs measure in the finite volume {1,..., n} and is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie–Weiss random-field Ising model (having singular paths).     

The analytic structure of the anomalous dimension of the four-gluon operator in deep inelastic scattering

The phenomenology of the pseudoscalar (1440) meson (also known as l) is discussed in a simplified , l mixing scheme in which the is assumed to have no glueball component. The parameters of the model are quite well constrained from the and two-photon decays. First it is shown that the scheme is in rather good general agreement with (almost) all the available data. Then a number of testable predictions concerning decays involving the iota are made. The iota turns out to be largely a glueball in this model.     

The theory of melting in heteropolymers. I. Random chains

A method is developed for the calculation of the ground-state melting curves ( _o vs.T) for random, infinite heteropolymers. Here _o is the ground-state value of the fraction of melted links ( _o in the strong cooperativity approximation). It is shown that the differential melting curves (d /d T vs.T) can have a fine structure in the form of several peaks on the bell-shaped main curve. Positions, magnitudes, and widths of these peaks are estimated. The accidental fine structure of melting curves, which is caused by a finite length of the polymer, is briefly discussed.Work supported in part by NSF Material Research Laboratory at Case Western Reserve University.Part of this work was submitted to the faculty of the Graduate School at SUNY Buffalo in partial fulfillment of the requirements for the Ph.D. degree.     

The mixing of elementary particles and the mass formula for bosons

The paper deals with the possibility of the existence of — ₂ mixing and the question of the Gell-Mann-Okubo formula (GOF) for bosons.     

Theoretical Study for Wavelength Conversion of Cascaded Second-Order Nonlinearity in Silica Fiber

In this paper, A novel wavelength divison multiplexing (WDM) nets is proposed by use of cascaded second-order nonlinearities (⁽²⁾:⁽²⁾) in the D-fiber grating after periodically thermal/electric-field poling, and is theoretically analyzed for the first time. The coupled mode equations of the ⁽²⁾:⁽²⁾ nonlinearities are derived, and the analytic expressions for the electric-field amplitude of converted light wave and the conversion efficiency are obtained under the small signal approximation, which are well consistent with numerical calculations. Both analytic expressions and numerical results show that, under the phase matching, is proportional to the logarithm of the square of pump light power, and the 4th power of the grating length L and the second-order nonlinearity d. The calculated results also show that and of this fiber grating can be reached over -17dB and 120nm, respectively. With the increase of L, increases rapidly while decreases quickly. The results of simulated calculations and theoretical analysis show that the cascaded ⁽²⁾:⁽²⁾ process is different from quasi-phases-matched difference-frequency generation.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Multiple coherent scattering of γ-radiation

Conclusions Multiplying (5) by 2d and integrating over angle, we get the relationship between the total flux and depth in the form , where .A similar result is obtained from integration of (11) over the angles and integration of (12) over the plane z = const. It thus follows that if we are interested in the angular distribution for in the first two cases and in the radial distribution for z in the third case, we can make an approximate estimate of the coherent scattering by eliminating the appropriate term from. This approach has been used in [15 etc.] but no indications were given of the conditions under which this is permissible.For problems in which small angles or small distances from the axis of a collimated source are important, allowance for the coherent scattering can change the result by an order of magnitude or more. For angles and it is possible to consider only the coherent scattering and to use (5), (11), and (12). For angles >gh and scattering >z, the contribution from coherent and incoherent scattering can be comparable. The kinetic equation must then be solved with allowance for both effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 129–132, May, 1973.     

Gravity of Global U(1) Cosmic String

We show that a static one-dimensional U(1) global string is confined by its own gravitational field to a finite radius. The energy-momentum tensor of a global string decreases exponentially with the distance from its core. We call it self-localization. We show that the order parameter is a decreasing function of the symmetry breaking energy scale. We have found the maximum value of the energy scale _max, where the order parameter vanishes. Beyond the maximum value > _max the gravitational field of a global string gets so strong, that it restores the initial unbroken symmetry. In the close vicinity of the maximum value _max of the symmetry breaking scale we get a closed-form solution for the metric. It reduces to the Galileo metric on the axis and transforms into the Kasner-type solution near the boundary of a string.     

Relativistic effects in decay of S-wave quarkoniums

The width of S-wave quarkonium decays (_c, _b ; and J/, Y e⁺e^–) are calculated using the quasipotential approach. The nontrivial dependence of decay amplitude on relative quark momentum is considered. It is shown that relativistic corrections reach values of 30–50% in the processes studied.Samara State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 46–53, May, 1995.     

Fatigue of Sb-Cs photocathodes

This experimental work deals with the influence of fatigue on the properties of the antimony cesium (Cs₃Sb) photocathode sensitized with oxygen. Photocells of special construction were prepared for the measurement and they were fatigued by illuminating them with white light from a tungsten lamp. The effect of fatigue on the spectral response curve, on the optical properties, values of activating energies, type of conductivity, current-voltage curves and integral sensitivity were investigated. In connection with the fatigue a shift of the long wavelength threshold towards shorter wavelengths, a decrease of response in the whole spectral range, changes in absorption and a drop in the value of the refractive index were observed. The maximum values of the activation energies, determined from measurements of the temperature dependence of the dark conductivity did not change. The conductivity of the photocathode was found to be of thep-type. The fatigue had certain effects on the current-voltage curves, the starting point of the anode current and the saturation point showing a certain shift towards lower positive anode voltages with fatigue. The relation between the fatigue and temperature rise of the photocathode due to the absorption of radiation was investigated. Finally some problems related to the mechanism of photoemission from the photocathodes are discussed.

---

Sb-Cs

- Cs₃Sb. , . , , , , - . , , , . , , . p. - : . . , .

     

On the positivity of the effective action in a theory of random surfaces

It is shown that the functional , defined onC functions on the two-dimensional sphere, satisfies the inequalityS[]0 if is subject to the constraint . The minimumS[]=0 is attained at the solutions of the Euler-Lagrange equations. The proof is based on a sharper version of Moser-Trudinger's inequality (due to Aubin) which holds under the additional constraint ; this condition can always be satisfied by exploiting the invariance ofS[] under the conformal transformations ofS ². The result is relevant for a recently proposed formulation of a theory of random surfaces.On leave from: Istituto di Fisica dell'Università di Parma, Sezione di Fisica Teorica, Parma, Italy     

Crossover critical correlation function

The anomalous dimension index assumes its critical value for small momenta and vanishes for large momenta. We provide, in the form of a quadrature, a momentum dependent (k) which interpolates between the above limits. High- and low-momentum expansions for the spectral function are obtained, leading to a Padé approximant from which (k) is determined, thereby giving a crossover critical correlation function.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday