Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

A quasi-likelihood approach for ordered categorical data with overdispersion

Quasi-likelihood (QL) methods are often used to account for overdispersion in categorical data. This paper proposes a new way of constructing a QL function that stems from the conditional mean-variance relationship. Unlike traditional QL approaches to categorical data, this QL function is, in general, not a scaled version of the ordinary log-likelihood function. A simulation study is carried out to examine the performance of the proposed QL method. Fish mortality data from quantal response experiments are used for illustration.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Ultrasonic attenuation in strongly disordered electronic systems

The attenuation of long-wavelength phonons due to their interaction with electronic excitations in disordered systems is investigated here. Lattice strain couples to electronic stress, and thus ultrasonic attenuation measures electronic viscosity. The enhancement and critical divergence of electronic viscosity due to localization effects is calculated for the first time. Experimental consequences for the anomalous increase of ultrasonic attenuation in disordered metals close to the metal-insulator transition are discussed. In the localized regime, the appropriate model is one of electronic two-level systems (TLS’s) coupled to phonons. The TLS consists of a pair of states with one localized state occupied and the other unoccupied. The density of such low-excitation-energy TLS’s is nonzero due to long-range Coulomb interactions. The question of whether these could be significant low-energy excitations in glasses is touched upon.

A Conjecture Concerning Transformation Of A Supercooled Hard-Sphere Liquid To A Metastable Disordered Solid

It is conjectured that the hard sphere system has several distinct solid phases, all but one of which are metastable. The bifurcation theory analysis of freezing is extended to the description of the transition between a supercooled liquid and a disordered solid by defining a restricted phase space for the disordered solid. This approach leads to the prediction of a first order transition between a supercooled hard sphere fluid and a disordered metastable hard sphere solid. The results of the calculation are in qualitative agreement with the results of Woodcock's molecular dynamics computer simulations. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Self-Organization of n-Alkane Chains in Water: Length Dependent Crossover from Helix and Toroid to Molten Globule

We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.

Vacancy ordered phases and one-dimensional quasiperiodicity

The metastable vacancy ordered phases observed in aluminium transition metal alloys on rapid solidification or vapour deposition can be considered as a periodic arrangement of a truncated quasiperiodic string based on the Fibonacci sequence along the left angle bracket111right-pointing angle bracket stacking direction of the original CsCl cell. Using the projection formalism developed in the context of quasicrystals, the diffraction patterns of the vacancy ordered phases are calculated for both commensurate and incommensurate projection from a periodic cubic cell in four dimensions. These are compared with experimentally observed patterns. It is shown that at increasingly longer periodicity the patterns from commensurate crystals become indistinguishable from the truly quasiperiodic one. It is suggested that there is a strong link between vacancy ordered phases and quasicrystals.

Electric-field-dependent average resistance and the resistance fluctuation in one-dimensional disordered systems

Following an invariant-imbedding approach, we obtain analytical expressions for the ensemble-averaged resistance (ρ) and its Sinai’s fluctuations for a one-dimensional disordered conductor in the presence of a finite electric field F. The mean resistance shows a crossover from the exponential to the power-law length dependence with increasing field strength in agreement with known numerical results. More importantly, unlike the zero-field case the resistance distribution saturates to a Poissonian-limiting form proportional to A‖F‖exp(-A‖F‖ρ) for large sample lengths, where A is constant.

Constant conductance fluctuations in disordered metals

We discuss the effect of fluctuations of the random potential in directions transverse to the current flow in a modified Migdal-Kadanoff approach to probabilistic scaling of conductance with size L, in d-dimensional metallic systems. The conductance cumulants are finite and vary as Ld−1−n for n greater-or-equal, slanted 2 i.e. conductance fluctuations are constant for d = 3. The mean conductance has a non-classical correction with Image Full-size image (<1K) for d greater-or-equal, slanted 2. The form of the higher cumulants is strongly influenced by the transverse potential fluctuations and may be compared with the results of perturbative diagrammatic approaches.

An Electron-Microscopic Investigation Of Oxides Related To Beta-Alumina

High resolution electron microscopic (HREM) investigation of potassiumbeta-alumina and the related gallate and ferrite has revealed that whereas the aluminate and gallate are highly disordered, consisting of random sequence ofbeta andbetaPrime units, the ferrite is more ordered. The aluminate and gallate are sensitive to electron beam irradiation exhibiting beam-induced damage similar to sodiumbetaPrime-alumina. Significantly, the ferrite is beamstable, the difference in behaviour amongst these related oxides arising from the different mechanisms by which alkali metal nonstoichiometry is accommodated. Barium hexaaluminate and hexaferrite are both highly ordered; specimens prepared by the barium borate flux method exhibit a new radic3a×radic3a superstructure of the hexagonal magnetoplumbite cell.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Insulating phase of a disordered system: Fermi glass versus electron glass

The authors examine the critical divergence of the low-frequency conductivity of the noninteracting Fermi glass and interacting electron glass models of the insulating phase of a disordered system as the metallic phase is approached. Results for the two are found to be rather different, which can be tested experimentally. In particular, for the electron glass, there exists a nonvanishing contribution to the dielectric constants from the low-frequency (hopping) conductivity even at low temperatures, which scales with the high-frequency (optical) contribution, and diverges with the same exponent at the insulator-metal transition.

Nature of ``Disorder'' in the Ordered Double Perovskite Sr2FeMoO6

The degree of B/B alternate cation order is known to heavily influence the magnetic properties of A2BB O6 double perovskites although the nature of such disorder has never been critically studied. Our detailed x-ray absorption fine structure studies in conjunction with synchrotron radiation x-ray diffraction experiments on polycrystalline Sr2FeMoO6 samples with various degrees of disorder reveal that a very high degree of short range order is preserved even in samples with highly reduced long range chemical order. Based on these experimental results and with the help of detailed structural simulations, we are able to model the nature of the disorder in this important class of materials and discuss the consequent implications on its physical properties.