Optic nonlinearities of a copper complex of pyrazinoporphyrazine

For the copper complex of pyrazinoporphyrazine AzaPhcCu(C(CH₃)₃)₈ in CH₂Cl₂, we use nanosecond pulses to measure its third-order nonlinear optic effects at 532 nm. The results show that its effective third-order nonlinear refractive index n ^eff ₂ (–7.85 × 10^–10 esu) is larger than that of the AzaPhcCu(C₁₂H₂₅)₄ and the CuPc(OC₅H₁₁)₈. The reverse saturable absorption (RSA) of AzaPhcCu-(C(CH₃)₃)₈ is demonstrated by the ratio of effective excited state to ground state absorption cross sections. The observed intersystem crossing lifetime _isc of AzaPhcCu(C(CH₃)₃)₈ (15 ns) and AzaPhcCu(C₁₂H₂₅)₄ (45 ns) are longer than that of CuPc(OC₅H₁₁)₈ (5.0 ns). The aza-substituents are suggested to form a S₁(n, ^*) state as their lowest excited singlet-states, and their radiationless intersystem crossing rates (1/_isc) are discussed with the spin-orbit coupling _S|H _SO|_T and the vibronic coupling _S|_T effects between S₁ and T₁ states.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

Interpretation of the a0(980) meson as a four-quark system

Quantum chromodynamics methods are used to calculate the section of the reaction a₀ ⁰ with formation as an intermediate state of the meson a₀(980), which is interpreted as a bound state of two quark-antiquark pairs, formed upon dissociation of two virtual photons, with which an electron and positron are exchanged in incident e^–- and e⁺-beams. It is shown that the a₀ 2⁰ decay is significantly more suppressed than the a₀ ⁰ decay.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–23, July, 1991.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Transverse waves in a relativistic rigid body

We present relativistic elasticity as a scalar field theory. We apply it to rigid bodies, i.e., relativistic bodies with a nonlinear elastic law and a definite longitudinal wave velocity _l equal to the light velocity,c. We obtain the transverse wave equation with a definite velocity _t , and the relation between _l , _t , and the Poisson coefficient is the classical one. This is an indication that we have the relativistic extension of a classical Hooke elastic law.     

Radiation damping of waves in a cold magnetized two-component plasma

It is shown in this paper that the damping decrements of electromagnetic waves with right circular polarization and the decrements of plasma oscillations near the cyclotron and hybrid frequencies in a strong magnetic field _eBpe are proportional to the square of the cyclotron frequencies _eB and _iB. In a weak magnetic field _eBpe the damping decrements of all modes are proportional to the square of the plasma oscillation frequencies _pe, _pi. Taking account of ions results in a nonzero damping decrement for electromagnetic waves with left circular polarization.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 8–11, October, 1982.In conclusion, I am grateful to L. S. Kuz'menkov and P. Polyakov for constant attention to the research and for useful remarks.     

A two-dimensional Fokker-Planck equation degenerating on a straight line

By an example of a two-dimensional hydrodynamic system, second-order Langevin equations with two correlated noise sources are investigated. It is shown that the asymptotic expression (t) for the stationary distribution functionP depends on the order in which the limiting transitions;t andN ₂₂0 (N ₂₂ is the power of one of the noises) are made. Using the method of local expansions in trigonometric form, approximate expressions are written for the distribution functionP at small but finiteN ₂₂ tending atN ₂₂0 to the known exact solution.     

On the question of the existence of a canonically defined distance function for metrics with indefinite signature on a given manifold

Let be the set of all inner products with a given indefinite signature on a finite-dimensional vector spaceV. It is shown that any continuous pseudometricd on which is canonical, i.e., invariant with respect to all automorphisms ofV, is of the formd(g, h)=f( _g / _h ), where _g , _h denote the volume elements associated withg andh, respectively, andf is a real-valued function; i.e., there are no nontrivial distance functions. This result shows that a reasonable distance function between metric fields on a manifoldM cannot be obtained in terms of canonical distances of the inner products induced in the tangent spaces. A similar result is proved even for uniform structures instead of pseudometrics.     

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH _N ^Q and a class of appropriate initial states such that if c is such an initial state, then _Q ^N (t)=exp(–1H _N ^Q t) _Q ^N (0) correctly describes at timest ₃,t ₆,,t _3N model states that correspond to the completion of the first, second, , Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time interval aroundt ₃,t ₆,,t _3N, the machine part of _Q ^N (t) is stationary.     

Periodic nonlinear waves on a half-line

Nontrivial solutions of the equationu _tt=u _xx–g(u) which are 2-periodic int and which decay asx are shown to exist ifg(a)=0 andg(0)>1. Breather-like solutions, which also decay asx –, can be interpreted as homoclinic solutions in thex-dynamics; their existence is still in question for generalg.     

Transport of light radiation in a spatially finite three-dimensional scattering medium

We propose a new method for solving radiation transport problems, which permits including in analytic form for the case of normal incidence the effect of spatial finiteness of the scattering medium. The formation of the light field accompanying changes in the optical parameters and optical dimensions of the medium is analyzed.this paper, we examine the simplest case of a geometry of a scattering medium in the form of a parallelipiped with optical length _x, height _y, and width _z. The analysis is performed for the case =1, _y = _z with the latter varying in the range 0.1 to . The results obtained show that the light field depends strongly on the optical dimensions of the medium. The limiting values of the optical dimensions (_y = _z), beginning with which the spatial finiteness of the medium can be neglected, are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Fizika, No. 8, pp. 82–85, August, 1982.     

Cantor spectrum and singular continuity for a hierarchical Hamiltonian

We study the spectrum of the HamiltonianH onl ₂() given by (H)(n)=(n+1)+(n–1)+V(n)(n) with the hierarchical (ultrametric) potentialV(2 ^m (2l+1))=(1–R ^m )/(1–R), corresponding to 1-, 2-, and 3-dimensional Coulomb potentials for 0<R<1,R=1 andR>1, respectively, in a suitably chosen valuation metric. We prove that the spectrum is a Cantor set and gaps open at the eigenvaluese _n (1)<e _n (2)<...<e _n (2 ⁿ –1) of the Dirichlet problemH=E, (0)=(2 ⁿ )=0,n1. In the gap opening ate _n (k) the integrated density of states takes on the valuek/2 ⁿ . The spectrum is purely singular continuous forR1 when the potential is unbounded, and the Lyapunov exponent vanishes in the spectrum. The spectrum is purely continuous forR<1 in (H)[–2, 2] and =0 here, but one cannot exclude the presence of eigenvalues near the border of the spectrum. We also propose an explicit formula for the Green's function.Work supported by the Fonds National Suisse de la Recherche Scientifique, Grant No. 2.042-0.86 (H.K. and R.L.) and 2.483-0.87 (A.S.)On leave from the Dipartimento di Fisica, Università degli Studi di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy     

jj-Type of coupling in the scheme to construct the energy levels of a shallow acceptor in semiconductors

There is examined the classification of shallow acceptor energy levels by jj-type coupling, whose wave functions are converted by sets of irreducible representations by one of the subgroupsD _4h ^/ ,D _3d ^/ ,D _2h ^/ of the group o _h ^/ . The representations ₅ ⁺ of the groupD _4h ^/ are obtained in the one-function approximation by using a variational method, and systems of eight radical second-order differential equations are solved for two functions ₅ ⁺ in the case of a shallow acceptor in germanium by the method of orthogonal differential factorization. A comparison is made of the two low levels found and their radial functions for each of the functions ₅ ⁺ with the computed levels and the functions of LS-type coupling.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 103–107, September, 1981.The authors are grateful to N. P. Konyukhova for great assistance in the numerical solution of the system of radial equations.     

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.     

Experimental study of the nonlinear properties of the surface-kink instability of a semiconductor plasma in a germanium plate

Experiments are reported on the characteristics of the surface-kink instability in germanium plates. The amplitude of the current and potential oscillations, the frequency, and the modulus of the wave vector of the wave are analyzed as functions of the electric field E and the magnetic induction B at 78, 300, and 350°K. The amplitudes of the current and potential oscillations, and also the frequencies, increase with increasing E and B, eventually reaching saturation. At E = const, the modulus of the wave vector is independent of B. It is shown that slightly above the threshold electric field or threshold magnetic induction, i.e., at a small value of [g = (E – E_t)/E_t 1, _B = (B – B_t)/B_t 1], the curves of the oscillation amplitude vs _E; B are linear in logarithmic scale. The slope of the lines is about 0.5, implying a soft excitation of the surface-kink instability in the plates.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 72–75, July, 1984.     

Isometric motions of a perfect charged fluid

Space-times with perfect charged fluids as sources, that admit groups G_r of isometric motions, are investigated. It is assumed that the velocity vector of the fluid is collinear to the timelike Killing vector ⁱ of group G_r. It is shown that the macroscopic motion of a perfect charged fluid can occur only in the direction of such a Killing vector ⁱ that defines an operator in an invariant subgroup or, in particular, an operator of the center of the group. Parametric representations of the generalized equations of state for the pressure p, the energy density of the fluid, , and the electric charge density are established. All these quantities are functions of the norm of the Killing vector ⁱ and the projection of the 4-potential of the electromagnetic field onto this vector ⁱ. In the approximation of the weak field in the coordinate system where ⁱ= ₄ ⁱ , these functional dependences imply that p, , and are functions of Newtonian and electrostatic potentials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–29, October, 1987.     

Possibility of a Lifshitz phase transition in Cd observed by a singularity in the muon Knight shift

During the past much effort has been devoted to a systematic study of the muon Knight shiftK in metallic environments and its implications on the local electronic structure of hydrogen in metals [1]. These measurements in simple metals were essentially all carried out in polycrystalline samples at room temperature. The present measurements in Cd in polycrystalline and single crystal samples cover a temperature range between 20 K and the melting point of this strongly anisotropic metal (hcp crystal structure,c/a ratio 1.89 — idealc/a ratio 1.63). These measurements add qualitatively new and interesting aspects and insights on the screening of a light hydrogen isotope in a metal as well as on certain properties of the host material itself. The outstanding features of the muon Knight shift in Cd are: (i) a strong intrinsic temperature dependence with an increase ofK of more than 100% between 20 K and the melting point (T=593 K), (ii) an anomaly at 110 K in the form of a singularity in the isotropic part ofK which is interpreted as a band structure effect, (iii) an anisotropic Knight shift contribution fitting the expressionK(T,)=K _iso(T)+K _ax(T) * (3 · cos² –1)/2, where both, the isotropic and the axial contribution ofK , are strongly temperature dependent.     

The equilibrium thermodynamics of a spin-boson model

We consider the equilibrium thermodynamics of a Dicke-type model forN identical spins of arbitrary magnitude interacting linearly and homogeneously with a boson field in a volumeV _N, in the limitN,V _N, withN/V _N=const. The system exhibits a second-order phase transition; complete information on the spin polarizations and their correlations is obtained. The proofs use a general result on the free energy of quantum spin systems based on the large deviation principle and the Berezin-Lieb inequalities.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Self-Similar Decay in the Kraichnan Model of a Passive Scalar

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field that is stationary and white noise in time, but fractional Brownian in space with roughness exponent 0<<2, appropriate to the inertial-convective range of the scalar. We find all self-similar solutions by transforming the scaling equation to Kummer's equation. It is shown that only those scaling solutions with scalar energy decay exponent a(d/)+1 are statistically realizable, where d is space dimension and =2–. An infinite sequence of invariants J _p, p=0, 1, 2,..., is pointed out, where J ₀ is Corrsin's integral invariant but the higher invariants appear to be new. We show that at least one of the invariants J ₀ or J ₁ must be nonzero (possibly infinite) for realizable initial data. Initial datum with a finite, nonzero invariant—the first being J _p—converges at long times to a scaling solution _p with a=(d/)+p, p=0, 1. The latter belongs to an exceptional series of self-similar solutions with stretched-exponential decay in space. However, the domain of attraction includes many initial data with power-law decay. When the initial datum has all invariants zero or infinite and also it exhibits power-law decay, then the solution converges at long times to a nonexceptional scaling solution with the same power-law decay. These results support a picture of a two-scale decay with breakdown of self-similarity for a range of exponents (d+)/<a<(d+2)/, analogous to what has recently been found in the decay of Burgers turbulence.