Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

Non-commutative Low-dimension Spaces and Superspaces Associated with Contracted Quantum Groups and Supergroups

Quantum planes, which correspond to all one-parameter solutions of Quantum Yang-Baxter Equation (QYBE) for the two-dimensional case of GL-groups, are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum h-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup G L _q (12) and corresponding quantum superspace C _q (12) are considered in Cartesian basis. The contracted quantum superspace C _h (12);) is interpreted as the non-commutative analog of the superspace with the fiber odd part.     

The number of bound states of singular oscillating potentials

For a spherically symmetric potential such that rVL ¹(a, ), a>0, and is such that, if we define W=– _r V(t) d(t), W belongs to L ¹ (0, ) and rW0 as r0, we show that the number of bound states in any partial-wave satisfies the bound n2 ₀ r W ² dr. It was shown in a previous paper [1] that this class of potentials is regular from the point of view of abstract scattering theory as well as from the time-independent theory and the Jost function approach. We show also that, for large values of the coupling constant, n(gV) has the asymptotic behaviour C _±g ₀ W(r) dr as g±.     

Zeta functions and transfer operators for piecewise monotone transformations

Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function (z) of (T, g) extends meromorphically to {z<^-1} (where =lim g^°T^n-1...g^°Tg ^1/n ) and thatz is a pole of if and only ifz ^–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation

This paper deals with the trend to equilibrium of solutions to the spacehomogeneous Boltzmann equation for Maxwellian molecules with angular cutoff as well as with infinite-range forces. The solutions are considered as densities of probability distributions. The Tanaka functional is a metric for the space of probability distributions, which has previously been used in connection with the Boltzmann equation. Our main result is that, if the initial distribution possesses moments of order 2+, then the convergence to equilibrium in his metric is exponential in time. In the proof, we study the relation between several metrics for spaces of probability distributions, and relate this to the Boltzmann equation, by proving that the Fourier-transformed solutions are at least as regular as the Fourier transform of the initial data. This is also used to prove that even if the initial data only possess a second moment, then _v>R f(v, t) v² dv0 asR, and this convergence is uniform in time.     

Existence of solutions for Schrödinger evolution equations

We study the existence, uniqueness and regularity of the solution of the initial value problem for the time dependent Schrödinger equationiu/t=(–1/2)u+V(t,x)u,u(0)=u ₀. We provide sufficient conditions onV(t,x) such that the equation generates a unique unitary propagatorU(t,s) and such thatU(t,s)u ₀C ¹(,L ²) C ⁰(H ²( ⁿ )) foru ₀H ²( ⁿ ). The conditions are general enough to accommodate moving singularities of type x^–2+(n4) or x^–n/2+(n3).     

Optical and magneto-optical effects in semi-conductor crystals

The complicated line structure of the fundamental absorption edge and the effect of magneto-optical oscillations (which are general properties of crystals) open up good possibilities for the study of band structure and exciton states.From a survey of the facts observed lately it follows that the real existence of the exciton is almost certain although no experiment has yet been performed, which would provide direct experimental proof of its motion in the crystal. The evidence of the motion of excitons in the crystal can be determined from effects based on spatial dispersion effects. The observed optical anisotropy of absorption in a Cu₂O cubic crystal (due to spatial dispersion) and the quadrupole character of the exciton linen=1 confirm the motion of exciton through the crystal.The fine structure of the spectral curve for photoconductivity (an effect that is also common to all crystals), which is directly connected with the exciton absorption structure, also testifies to the motion of excitons.The exciton structure of the absorption edge and also the connected effect of edge emission enable the band structure and its splitting to be studied.The determination of the splitting of the exciton lines and edge of continuous absorption under the influence of oriented elastic deformation and the study of the state of polarization of the split components provides a new method for the study of band structure.The study of the Zeeman effect for lines of exciton, absorption in crystals can supply data on the exciton motion and on the complicated band structure in crystals. Special detailed data on the band structure can be obtained from studies in polarized light. From the effect of magneto-optical oscillations we can decide with great exactness the band width of the forbidden zone and obtain data which are in good agreement with those obtained by other methods.

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- , , . , , , , . , . — —, , n=1 . — , , — , . , - . () , . , , , , . - . . , , .

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Address delivered at International Conference on Semi-conductor Physics, Prague, Czechoslovakia, September 1960.     

ИЗЛУЧЕНИЕ ЧЕРЕНКОВА ПРОСТРАНСТВЕННОГО З АРЯДА В ВОЛНОВОДАХ И В НЕОГР АНИЧЕННОЙ СРЕДЕ

, - e . -. , .     

Weak four-fermion interaction in terms of SU(3) invariants. II

A lepton octet is constructed by analogy with the baryon octet by the substitution p⁺N ₁e⁺,⁺₁ é⁺,^-₂^-, ^- N ₂^-, where ₁, ₂,N ₁,N ₂ are arbitrary constants. The neutral components are replaced by a linear sum of the electron and muon neutrinos with arbitrary coefficients. The constants are determined from the system of general conditions (normalization, absence of crossed terms of the type ( etc.). As a result, the lepton octet is determined to within a single constant, and this is shown to be identical with the Cabibbo angle. Calculations are also made of the weak decays of baryons of the octet in the case of both charged and neutral currents. In the case of charged currents, the results agree with Cabibbo's theory. Calculations are also made of the lepton-lepton weak interactions and the ratios of the corresponding constants are determined. The ratios are in qualitative agreement with the existing experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–56, January, 1976.     

An attempt at a phenomenological interpretation of the influence of a polarizing field on piezoelectric resonators

The change in frequency of quartz piezoelectric resonators in a d-c electric polarizing field cannot be explained merely by a change in the dimensions of the resonator due to the polarizing field caused by the inverse piezoelectric effect and electrostriction. We are forced to admit that the elastic constants also change in a polarizing field. A phenomenological interpretation of the influence of a d-c electric polarizing field on the frequency of quartz resonators is proposed here, based on newly introduced quantities characterizing such a change. In conclusion it is shown in what way the quantities, on which the phenomenological theory is based, can be determined experimentally.

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, . , . , , . , , .

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The author would like to thank Dr. J. Tichý for carefully reading the paper, for valuable discussion and numerous remarks on style and subject matter, which greatly helped to improve the text. He is also indebted to V. Janovec, C. Sc., for some new aspects and the exceptional interest with which he reviewed the paper.     

Correlation functions and the Goldstone picture for the hierarchical classical vector model at low temperatures in three or more dimensions

Low-temperature properties of the one-and two-point correlation functions are obtained for the pure state classical vector model in a hierarchical formulation. We consider theZ ^d lattice model (d3) where the single-site spin variableR ^v has a density proportional to for large. We obtain the pure state one- and two-point functions by introducing a uniform magnetic field which goes to zero as the volume goes to infinity. Using renormalization group methods, we generate a sequence of effective actions and spin variable and determine the spontaneous magnetization (one-point function parallel to the field). We confirm the Goldstone picture by showing that the truncated two-point function has the canonical massless decay x–y^–(d–2) x,yZ^d in the directions perpendicular to the field. We show a faster decay in the parallel direction and for larged that the decay is x-y^–(d+2).Research support by CNPq, Brazil.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Polarization of strangeness Arizona muon

The longitudinal polarization of strangeness Arizona muon, namely, the 236 MeV/c ⁺ from the K^{+ +} v decay, has been measured to search for right-handed weak current in the strangeness changing process. The polarization has been determined to be –0.967±0.047.We are grateful to Professors T. Nishikawa, S. Ozaki, A. Kusumegi, and H. Sugawara of KEK for their encouragement and support during the course of this experiment. We are grateful to the operating crew of the KEK proton synchrotron and its experimental facilities for their cooperation during the experiment. This work is partially supported by the Grant-in-Aid of the Ministry of Education, Science and Culture.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

Multiatom interactions,order and stability in binary transition metal alloys

Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the t^–1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.