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.     

Duality for a Lorentz quantum group

We give the algebra _q ^/* dual to the matrix Lorentz quantum group _q of Podles-Woronowicz, and Watamuraet al. As a commutation algebra, it has the classical form _q ^/* U _q (sl(2, )) U _q (sl(2, )). However, this splitting is not preserved by the coalgebra structure which we also give. For the derivation, we use a generalization of the approach of Sudbery, viz. tangent vectors at the identity.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Renormalized transport equations for the bistable potential model

Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value x _t can be evaluated in both domains Dx _± and xD ₀ outside and between the potential minima, leading to drastic differences of the dynamics prevailing inD _± andD ₀, respectively.     

Induced geometry and confinement

A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric _v , an induced metricg _v that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong _v due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given.     

Phase transitions in 2-dimensional systems of migrating orientable lattice defects

Phase transitions are studied in a system consisting of reorientating and migrating point defects in a two dimensional lattice. Due to the long range (r ^–2) nature of the dominant elastic interaction, surface effects are of central importance and have to be included. After diagonalizing the elastic interaction energy for defects characterized by arbitrary elastic dipole tensors the free energy of the system is minimized with respect to the tensor defect density (which describes the defect distribution in space and over a discrete number of orientations). Different types of phase transitions are obtained depending on the magnitude of the defect anisotropy. The phase below the paraelastic one is characterized for large by an anisotropic but homogeneous distribution, for small by an anisotropic and inhomogeneous distribution with a non linear space dependence. Similarities and differences with 3d results for=0 (or small) are discussed.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

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.     

The special status ofη 1 in QCD

On the basis of the approximate vanishing of the singlet axial charge of the nucleon, it is argued that ₁ should decouple from all hadrons constructed out of the constituentu, d ors quarks in theU(3) _L ×U(3) _R chiral limit for largeN _c . Furthermore ₁ should dominate the processesJ/, . A phenomenological analysis of the and couplings to many hadronic states is consistent with these results.     

On the correlation functions of fully frustrated two-dimensional Ising systems

By mapping the triangular antiferromagnet, the Villain model and the Union-Jack model on the quantumXY-chain we show a simple way to obtain the exponent =1/2 for the decay of the spin-correlation function at the frustration points of these models. A similar procedure for the Baxter model leads to non-universal values of .     

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.     

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.     

Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities

The eight-vertex model is equivalent to a solid-on-solid (SOS) model, in which an integer heightl _i is associated with each sitei of the square lattice. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a variable parameter . Here we begin by showing that the hard hexagon model is a special case of this eight-vertex SOS model, in which =K/5 and the heights are restricted to the range 1l _i4. We remark that the calculation of the sublattice densities of the hard hexagon model involves the Rogers-Ramanujan and related identities. We then go on to consider a more general eight-vertex SOS model, with =K/r (r an integer) and 1l _ir–1. We evaluate the local height probabilities (which are the analogs of the sublattice densities) of this model, and are automatically led to generalizations of the Rogers-Ramanujan and similar identities. The results are put into a form suitable for examining critical behavior, and exponents, , are obtained.Supported by the Guggenheim Foundation and in part by the National Science Foundation, grant MCS 8201733.     

Origin and manifestation of the anharmonic potential felt by an ion-cloud in an actual Paul trap

The anharmonic potential felt by a single-species ions confined in a rf quadrupole trap which results from a non-ideal trap configuration and the charge distribution of the ion cloud is studied. The rf resonance-absorption spectra are explained by a Duffing oscillator and a representation of the line-shape parameter is derived. For > 0.77, the electric signals will exhibit hysteresis. The relation with the anharmonic potential is discussed.     

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 .     

Basic Properties of Quantum Automata

This paper develops a theory of quantum automata and their slightly more general versions, q-automata. Quantum languages and -quantum languages, 0<1, are studied. Functions that can be realized as probability maps for q-automata are characterized. Quantum grammars are discussed and it is shown that quantum languages are precisely those languages that are induced by a quantum grammar. A quantum pumping lemma is employed to show that there are regular languages that are not -quantum, 0<1.     

Distribution of nuclear quadrupole splittings in amorphous materials and the topology of the (Vzz, η)-parameter space

In structural investigations of amorphous materials by determination of nuclear quadrupole splittings, the connectivity of the region of non-zero probability density in the space of the splitting parameters V_zz and is important. The conventional presentation of the parameter plane conceals the continuous connection between regions of positive and negative V_zz via the common boundary defined by =1. A new conceptual view of the (V_zz, )-plane is proposed which clearly expresses its topological structure.     

Levinson's Theorem for the Schrödinger Equation in One Dimension

Levinson's theorem for the one-dimensional Schrödinger equation with asymmetric potential which decays at infinity faster thanx ^–2 is established by theSturm-Liouville theorem. The critical case where the Schrödinger equation hasa finite zero-energy solution is also analyzed. It is demonstrated that the numberof bound states with even (odd) parityn ₊(n _–) is related to the phase shift ₊ (0)[_– (0)] of the scattering states with the same parity at zero momentum as ₊ (0)+ /2 =n ₊ and _– (0) =n _– for the noncritical case, and ₊ (0) =n ₊ and_– (0) – /2 =n _– for the critical case.     

Pseudopotential calculation of the energy of vacancy formation in binary alloys as a function of the degree of far order

Pseudopotential theory is used to study the dependence of energy of vacancy formation E_IV ^f in binary replacement alloys as a function of the degree of far order is shown that E _IV ^f =E_o+E·]², where E_o is the energy of vacancy formation in a disordered alloy, E then contains the ordering energy. It is shown with examples of the alloys CuZn, AuZn, and AgCd that the energy of vacancy formation can decrease with increase in the degree of far order. It is found that in calculating the vacancy formation energy it is necessary to consider lattice relaxation energy, since such consideration can lead to a change in the sign of E.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 62–67, June, 1984.     

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.