Universal conductance fluctuations in Sierpinski carpets

We theoretically investigate the conductance fluctuation of two-terminal device in Sierpinski carpets. We find that, for the circular orthogonal ensemble (COE), the conductance fluctuation does not display a universal feature; but for circular unitary ensemble (CUE) without time-reversal symmetry or circular symplectic ensemble (CSE) without spin-rotational symmetry, the conductance fluctuation can reach an identical universal value of 0.74±0.01(e²/h). We further find that the conductance distributions around the critical disorder strength for both CUE and CSE systems share the similar distribution forms. Our findings provide a better understanding of the electronic transport properties of the regular fractal structure.     

Transition curves for the variance of the nearest neighbor spacing distribution for Poisson to Gaussian orthogonal and unitary ensemble transitions

Using an appropriate 2x2 random matrix ensemble, transition curves for the variance of the nearest neighbor spacing distribution are constructed for the Poisson to Gaussian orthogonal and unitary ensemble transitions in terms of an easily identifiable transition parameter.     

Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping ofℝ ⁿ onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofℓcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine. A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper. Related results have been obtained by Borchers and Hegerfeldt. Received: 3 May 1999 / Accepted: 7 July 2000     

Essential Variational Poisson Cohomology

In our recent paper “The variational Poisson cohomology” (2011) we computed the dimension of the variational Poisson cohomology for any quasiconstant coefficient ℓ × ℓ matrix differential operator K of order N with invertible leading coefficient, provided that is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the -graded Lie superalgebra is isomorphic to the finite dimensional Lie superalgebra . We also prove that the subalgebra of “essential” variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K, is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case.     

Replica field theories,painlevé transcendents,and exact correlation functions

Exact solvability is claimed for nonlinear replica sigma models derived in the context of random matrix theories. Contrary to other approaches reported in the literature, the framework outlined does not rely on traditional "replica symmetry breaking" but rests on a previously unnoticed exact relation between replica partition functions and Painlevé transcendents. While expected to be applicable to matrix models of arbitrary symmetries, the method is used to treat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE (symmetry classes A and AIII in Cartan classification) and Ginibre's ensemble of complex non-Hermitian random matrices. Further applications are briefly discussed.     

Finite element distributions in statistical theory of energy levels in quantum systems

The probability density functions of the three-point finite elements of the three adjacent energy levels for the three-level quantum system are introduced as a supplementary characteristics of quantum chaos. The three-level quantum system is studied. The probability density functions of the second difference and asymmetrical three-point first finite element are computed for the three-dimensional Gaussian orthogonal ensemble GOE(3), the three-dimensional Gaussian unitary ensemble GUE(3), the three-dimensional Gaussian symplectic ensemble GSE(3), as well as for the Poisson ensemble PE.     

Random matrix model for disordered conductors

We present a random matrix ensemble where real, positive semi-definite matrix elements, x, are log-normal distributed, exp[−log²(x)]. We show that the level density varies with energy, E, as 2/(1+E) for large E, in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson’s Coulomb gas analogy breaks down whenever the confining potential is given by a transcendental function for which there exist orthogonal polynomials.     

Network reconstruction from random phase resetting

We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random phase resets of the system dynamics. The desired details of network structure are then revealed by appropriately averaging over the ensemble. The method is applicable for a wide class of networks with arbitrary emergent dynamics, including full synchrony.     

Conversion--electron gamma--ray coincidence spectroscopy of superdeformed 135Nd

Three mini-orange conversion–electron spectrometers and four Euroball Ge Cluster detectors have been used for γ–e^- coincidence spectroscopy of superdeformed ¹³⁵Nd. Transitions within the superdeformed band are shown to have the expected E2 multipolarity. The 766.5–keV transition which links the band to a positive-parity state has a conversion coefficient consistent with M1 multipolarity. Consequently, positive parity is deduced for the superdeformed band. No evidence for E0 transitions was found. Received: 22 December 1997 / Revised version: 19 January 1998     

Application of Raman scattering to study of anisotropy of molecular ensembles

A general expression is obtained for the Raman scattering intensity in an ensemble of diatomic molecules for an arbitrary geometry of the experiment as a function of the anisotropy of angular distribution of molecular axes. In its derivation, the irreducible representation of the density matrix of molecules was used. It is shown that, in the Raman scattering experiments on the study of the anisotropy of molecular ensembles, a significant contribution to the signal is made, not only by the second-order terms 〈cos²θ〉, but also by the fourth-order terms proportional to 〈cos⁴θ〉, which should be taken into account to correctly interpret the experimental data. Convenient experimental geometries are proposed that allow the anisotropy of a molecular ensemble to be investigated.     

Statistical properties of many-particle spectra: III. Ergodic behavior in random-matrix ensembles

The ergodic problem is defined for random-matrix ensembles and some conditions for ergodicity given. Ergodic properties are demonstrated for the orthogonal, unitary and symplectic cases of the Gaussian and circular ensembles, and also for the Poisson ensemble. The one-point measures, viz., the eigenvalue density, the number statistic and the k'thnearest-neighbor spacings are shown to be ergodic and the ensemble variances of the corresponding spectral averages are explicitly calculated. It is moreover shown, by using Dyson's cluster functions, that all the k-point correlation functions are themselves ergodic as are therefore the fluctuation measures which follow from them. It is proved also that the local fluctuation properties of the Gaussian ensembles are stationary over the spectrum.     

Normal modes and quality factors of shielded composite dielectric spherical resonators

Electromagnetic field analysis of shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials has been made. Characteristic equations for the TE_nmℓ and TM_nmℓ modes have been derived. From these characteristic equations, the resonant frequencies and quality factors have been calculated using numerical method. Computations of the resonant frequencies and quality factors have been made for resonators with parameters suitable for the optical and microware regions. In this paper we have presented the analysis and the results obtained from the numerical computations for shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials. Starting from the Maxwell’s equations for such a resonators have been derived and resonant frequencies and quality factor’s have been calculated for the TE_nmℓ and TM_nmℓ modes using numerical method.     

Analysis of the semileptonic Bc→Bu *ℓ+ℓ- decay from QCD sum rules

We analyze the semileptonic B_c→B_u ^*ℓ⁺ℓ^- decay in the framework of the Standard Model. We calculate the B_c to B_u ^* transition form factors in QCD sum rules. Analytical expressions for the spectral densities and gluon condensates are presented. The branching ratio of the B_c→B_u ^*ℓ⁺ℓ^- decay is calculated, and it is obtained that this decay can be detectable at forthcoming LHC machines. PACS 12.60.-i, 13.30.-a., 13.88.+e     

On an interpolation model for the transition operator for Markov and non-Markov processes

A phenomenological interpolation model for the transition operator of a stationary Markov process is shown to be equivalent to the simplest difference approximation in the master equation for the conditional density. Comparison with the formal solution of the Fokker-Planck equation yields a criterion for the choice of the correlation time in the approximate solution. The interpolation model is shown to be form-invariant under an iteration-cum-rescaling scheme. Next, we go beyond Markov processes to find the effective time-development operator (the counterpart of the conditional density) in the following very general situation: the stochastic interruption of the systematic evolution of a variable by an arbitrary stationary sequence of randomizing pulses. Continuous-time random walk theory with a distinct first-waiting-time distribution is used, along with the interpolation model for the transition operator, to obtain the solution. Convenient closed-form expressions for the ‘averaged’ time-development operator and the autocorrelation function are presented in various special cases. These include (i) no systematic evolution, but correlated pulses; (ii) systematic evolution interrupted by an uncorrelated (Poisson) sequence of pulses.     

Cholesteric pitch-transitions induced by a magnetic field in a sample containing incomplete number of pitches

We investigate the pitch transitions induced by an external bulk field in a Cholesteric Liquid Crystal slab of finite thickness ℓ that contains an incomplete number of π-twists. The analysis is performed for a magnetic field that is (i) perpendicular to the helical axis, and (ii) tilted with respect to one of the easy directions imposed by planar and rigid boundary conditions. For finite ℓ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time with increasing field to avoid divergences in the elastic energy. The dependence of the threshold magnetic field inducing the expulsion on the easy axes twist angle δ is investigated for all the cascade of pitch transitions and in particular for the final one, corresponding to the Cholesteric-Nematic transition. In the ℓ → ∞ limit this dependence disappears and we reobtain the results of de Gennes for an infinite sample.     

CP violation in the B→Kℓ<Superscript>+</Superscript>ℓ<Superscript>-</Superscript> decay

Standard model (SM) CP asymmetries in B→Kℓ⁺ℓ^- are expected to be very small. This feature could help in the understanding of new physics scenarios which predict the existence of CP odd phases in various Wilson coefficients. In this paper we have analyzed the B→Kℓ⁺ℓ^- decay in scenarios beyond the SM where the Wilson coefficients have new CP odd phases. The sensitivity of the CP asymmetries on these new weak phases is discussed. PACS 13.20.He; 12.60.-i; 13.88.+e     

Influence of annealing on the spatial distribution of thermoelectric properties in bismuth-telluride specimens

A p-type (Bi_0.25Sb_0.75)₂Te₃ specimen doped with 8 wt. % excess Te alone and an n-type Bi₂(Te_0.94Se_0.06)₃ specimen codoped with 0.017 wt. % Te and 0.068 wt. % I were grown by the Bridgeman method and were cut into a parallelepiped of 5×5×15 mm³, where the length of 15 mm is parallel to the freezing direction. Their local Seebeck coefficient α_ℓ and local electrical resistivity ϱ_ℓ were measured before and after annealing at a scan step of 1 mm along the freezing direction of the specimen, where annealing was done at 673 K for 2 h in vacuum. The specimen was mounted on an X–Y stage and the temperature difference between two probes set at an interval of 1 mm apart was approximately 2.6 K and measured with an accuracy of 0.1 K. The ϱ_ℓ of the as-grown and annealed specimens changed more significantly from place to place than their α_ℓ, so that the effect of annealing on the local power factor P_ℓ (=α_ℓ ²/ϱ_ℓ) was not uniform throughout the specimen surface. Such a spatial variation in P_ℓ is considered to result mainly from the spatial variation in ϱ_ℓ which originates from only a slight deviation of the melt composition from the stoichiometry inside a specimen, and also from a difference in the degree of alignment of the c planes of grains inside a specimen. The maximum P_ℓ (=α_ℓ ²/ϱ_ℓ) of the annealed p- and n-type specimens reached surprisingly high values of 7.78 and 8.93 mW/K² m, respectively, which correspond to being about twice as large as the macroscopic P values obtained by conventional methods. PACS 72.15.Jf; 84.60.Rb; 85.30.De     

Donor ordering and the statistics of quantum dot level spacings and widths from full 3D self-consistent electronic structure

Using full 3D self-consistent electronic structure calculations of small (electron numberN 100) lateral quantum dots formed on GaAs–AlGaAs HEMT devices we calculate the statistics of level spacings Δε_pand tunneling coefficients Γ_pbetween leads and confined states of the dot. We employ random and ordered donor layer charge distributions, the latter generated through Monte Carlo variable range hopping simulations, as well as a homogeneous (jellium) ionic charge distribution, and examine the effects on these statistics.It has recently been argued that the statistics of the level spacings and widths follow from random matrix theory when the Hamiltonian is described by the Gaussian orthogonal ensemble (GOE) for zero magnetic fieldB, and by the Gaussian unitary ensemble (GUE) forBsufficiently large to break time reversal symmetry. Specifically it is argued that when the dot wave functions are expanded in an arbitrary basis the expansion coefficients, according to the postulate of Porter and Thomas, are uniformly distributed in Hilbert space.In our calculation we obtain statistics of level spacings and widths by generating many configurations of disordered and ordered donor charge. This corresponds to the experimental situation of thermal cycling of the device. We find that a pronounced transition occurs in the level spacing statistics between the completely disordered donor layer ensemble, which seems to be well described by random matrix theory, and the ordered ensemble which is dominated by secular variations in the coefficients. In particular, a shell structure in the levels, which results from approximate parabolicity in the self-consistent confining potential, is observed. This, and the effects of symmetry under inversion and azimuthal symmetry, are speculated to undermine level repulsion and result in Poisson statistics for the levels here at the band edge.Finally we find that distortions in the dot shape are markedly less significant in varying the widths (and level spacings) than calculations based on a hard wall potential for the dot predict. This suggests that the notion of invariant atomic structure for sufficiently small dots is not invalidated by the randomness inherent in donor positions and shape distortion but, on the contrary, a systematic study of dot structure is possible.     

Density matrix for particle production processes in an external field

The general problem of finding the density matrices of particles and antiparticles produced by an external electromagnetic field fron an arbitrary initial state is solved. Expressions are obtained for the density matrices of particles and antiparticles produced from a state with given number of initial particles and from a state described by an initial grand canonical ensemble.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fiz., No. 6, pp. 77–81, June, 1980.