Conductance distributions in random resistor networks. Self-averaging and disorder lengths

The self-averaging properties of the conductanceg are explored in random resistor networks (RRN) with a broad distribution of bond strengthsP(g)g ^–1. The RRN problem is cast in terms of simple combinations of random variables on hierarchical lattices. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of sizeL and the distribution tail strength parameter . For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit 0. Adisorder length _D is identified, beyond which the system is effectively homogeneous. This length scale diverges as _Dµ^–v ( is the regular percolation correlation length exponent) when the microscopic distribution of conductors is exponentially wide (0). This implies that exactly the same critical behavior can be induced by geometrical disorder and by strong bond disorder with the bond occupation probabilityp. We find that only lattices at the percolation threshold have renormalized probability distributions in aLevy-like basin. At the percolation threshold the disorder length diverges at a critical tail strength µ_c as µ–^–z withz3.2±0.1, a new exponent.Critical path analysis is used in a generalized form to give the macroscopic conductance in the case of lattices abovep _c.     

Upper critical fields of single-crystalline and polycrystalline Ca-Sr-Bi-Cu-O compounds

The ac resistivity of a 110 K phase multiphase polycrystalline Ca-Sr-Bi-Cu-O compound and an 85 K phase single-crystalline Ca_0.9Sr_2.1Cu_2.0O_{8 +} has been measured in various magnetic fields up to 8 T. Values forB _c ^2/ (0) of 71.5 T and forB _c2 (0) of 542 T are found for the 85 K phase sample. A value forB _c2(0) of 57.9 T is estimated for the 110K phase compound.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

New cascade laser transitions in CH2F2 pumped with the 9R32 line of a cw CO2 laser

New cascade laser transitions of¹²CH₂F₂ at 172.50m, 208.83m, 220.44m, 223.99m and 250.61m are reported. A waveguide FIR laser was pumped with a quasi cw¹²C¹⁶O₂ laser operating on the 9R32 line. Together with the already known lines at 184.3m, 196.1m and 235.9m, the laser lines can be assigned to rotational transitions in the ₉ vibrational band of¹²CH₂F₂ and to refill transitions of the vibrational ground state ₀.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.     

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.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

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 .     

Trilinear generally covariant equations

Field equations for n-frames h ^a that are possible in the theory of absolute parallelism are considered. It is shown that in three cases the equations can, after the substitution h ^a =H^pH ^a (H=det H ^a , p is an n-dependent constant), be written in a trilinear form that contains only the matrix H _a and its derivatives and not H ^a . It is shown that the equations are still regular for degenerate but finite matrices H _a if rank H _a 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–27, February, 1991.     

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.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

Ultra-high piezoelectric response in 〈<Emphasis Type="Bold">110</Emphasis>〉- oriented polydomain Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>- PbTiO<Subscript>3</Subscript> single crystals

The piezoelectric constant and electromechanical coupling coefficients of 110-oriented polydomain0.71Pb(Mg_1/3Nb_2/3)O₃-0.29PbTiO₃ single crystals were determined experimentally by using resonance methods. It was confirmed that the single-crystal system has large electromechanical coupling coefficients k₃₃ (91%), k₃₃ (83%), and k₃₁ (81%), and piezoelectric constant d₃₃ (1400 pC/N), which are comparable to those of 001-oriented crystals, and we also found that the values of k₃₃ and k₃₁ are sensitive to the cuts of the crystals. X-ray-diffraction measurements on 110-oriented crystals have shown that the origin of the high piezoelectric response should be attributed to the orthorhombic distortion. Our results show that the 110-oriented crystals are also promising for a wide range of electromechanical transducer applications, since the 110-oriented crystals can be grown from 110-oriented seed crystals in the modified Bridgman technique. PACS 77.80.Bh; 77.84.Dy; 77.65.Bn     

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.