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.     

Dynamics of the generalized Glauber-Ising chain in a magnetic field

A one-dimensional kinetic Ising model with nearest neighbor interactionJ and magnetic fieldH 0 is treated in both linear and nonlinear response, using the most general single spin-flip transition probabilities that depend on nearest neighbor states only. The dynamics is reformulated in terms of kinetic equations for the concentration n_l ⁺(t) [@#@ n_l(t) of clusters containingl up- [or down-] spins, which is exact in the homogeneous case. The initial relaxation time ^* of the magnetization is obtained rigorously for arbitraryJ, H, and temperatureT. The relaxation function is found by numerical integration forJ/T < 2. It is shown that coagulation of minus-clusters becomes negligible for bothJ/T andH/T large, and the resulting set of equations is solved exactly in terms of an eigenvalue problem. A perturbation theory is developed to take into account the neglected coagulation terms. The relaxation function is found to be non-Lorentzian in general, in contrast to the Glauber results atH = 0, which are recovered as a special case. In addition, nonlinear and linear relaxation functions differ forH 0. Consequences for the application to biopolymers are briefly mentioned.Supported in part by the Deutsche Forschungsgemeinschaft (SFB 130).     

Continuous quantum measurements and the action uncertainty principle

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral in finite limits). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is S, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is | ^t (S[q]/q(t))q(t)dt|, where the paths [q] and [q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as (Equation) (Path) . This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

Study of the Β decay of6He with allowance for second-class currents and the antineutrino mass

The effects of the rest mass of the electron antineutrino are studied with allowance for the induced tensor form-factor F_c of the second-class current according to the Weinberg classification during the decay of the⁶He nucleus. We calculate the contribution of m and F_c to the electron-antineutron angular correlation coefficient A_e and the degree of longitudinal polarization P_e of the decay electrons. When m is nonzero, the coefficient A_e tends asymptotically to zero both at the beginning and endpoint of the spectrum, whether or not the second-class currents are taken into account. The series of qualitatively new experiments planned for the near future to measure the e- correlation for pure Gamow-Teller transitions (the⁶He nucleus could be a suitable nucleus here) with an accuracy of the order of 1% would allow the available estimate of the form-factor F_c to be improved substantially.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–67. September, 1989.     

Double cascade transitions of gamma rays from radiative capture on Co59

Pairs of gamma quanta, giving a sum equal to the binding energy of the last neutron in a Co⁶⁰ isotope, were studied during radiation capture on a Co⁵⁹ nucleus. The energies of the gamma quanta giving such cascades were determined and an attempt was made to determine the relative intensities of the different cascades.

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- Co⁵⁹

Co⁵⁹ -, Co⁶⁰. -, , .

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In conclusion the authors thank J. Vávra for cooperation in the measurements.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Two-frequency method for increasing the signal-to-noise ratio for nuclear quadrupole resonance14N low-frequency transitions

A method is proposed for increasing the signal-to-noise ratio during detection of NQR¹⁴N low-frequency transitions, consisting in a preliminary saturation of the _o(_–) transition before accumulation of the multiplet signals of the spin echo or induction signals, observed during the action of a series of 90 pulses on the _–(_o) transition. The gain in signal-to-noise ratio achieved by the two-frequency action is calculated theoretically, and the maximum value is found to be 3/(3 –) for _– and 3(1 + )/4 for _o. It is shown that the envelope of the induction signal for an increase in the time between the 90 pulses decreases according to one exponent for _o, while for _– and ₊ it decreases according to two exponents, and the approach to equilibrium of the system of¹⁴N nuclei is oscillatory in nature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 61–64, November, 1987.     

Diffusion of positive muons and other light particles in metals

The paper gives a survey of the principal techniques available for the experimental determination of the diffusivityD ⁺(T) of positive muons in crystals (Gurevich technique, trapping, longitudinal muon-spin relaxation, transverse muon-spin relaxation in superconductors) and discusses their strengths and weaknesses. The main theoretical ideas of the quantum theory of diffusion are outlined and the distinction between different mechanisms is emphasized. It is argued that at high temperaturesT the so-called adiabatic regime with a preexponential factor of the diffusivity of the order of magnitude _D d ² ( _D = Debye frequency of the host crystal,d=jump distance of the muons) always exists. In the fcc metals and in the case of¹H in Nb it is followed by a so-called Flynn-Stoneham regime at intermediate temperatures, whereas for ⁺ in Nb and-Fe such a regime is not observed. Instead, in these cases the adiabatic regime appears to go over directly to the few-phonon regime of incoherent tunnelling between adjacent ground states, leading to the one-phononD ⁺ ~T law at low temperatures.The metal best-studied with regard to muon diffusion,-Fe, is used to illustrate the theoretical analysis of experimental results in some detail. In an Appendix the theoretical expressions required for the quantitative determination ofD ⁺ by the Gurevich technique are collected.