On the Distribution of Surface Extrema in Several One- and Two-dimensional Random Landscapes

We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one-and two-dimensional substrates focusing our analysis on the probability distribution function P(M,L) of the number M of maximal points (i.e., local “peaks”) of growing surfaces. Our analysis is based on two central results: (i) the proof (presented here) of the fact that uniform one-dimensional ballistic growth process in the steady state can be mapped onto “rise-and-descent” sequences in the ensemble of random permutation matrices; and (ii) the fact, established in Ref. [G. Oshanin and R. Voituriez, J. Phys. A: Math. Gen. 37:6221 (2004)], that different characteristics of “rise-and-descent” patterns in random permutations can be interpreted in terms of a certain continuous-space Hammersley-type process. For one-dimensional system we compute P(M,L) exactly and also present explicit results for the correlation function characterizing the enveloping surface. For surfaces grown on 2d substrates, we pursue similar approach considering the ensemble of permutation matrices with long-ranged correlations. Determining exactly the first three cumulants of the corresponding distribution function, we define it in the scaling limit using an expansion in the Edgeworth series, and show that it converges to a Gaussian function as L → ∞.     

Magnetoexciton light absorption in inhomogeneous quasi-two-dimensional systems

The problem of exciton light absorption in quasi-two-dimensional inhomogeneous systems in a strong transverse magnetic field H is analyzed. We assume that a random Gaussian field (“white noise”) acting separately on an electron and a hole is due to (1) fluctuations in the quantum well thickness or (2) fluctuations in the concentrations of the solid solution components. The problem of a magnetoexciton in a random Gaussian white noise field has been reduced to the problem of the motion in an H-dependent effective field of a single particle with the effective magnetic mass of the exciton, which is a function of the magnetic field and parameters of the quantum wells, in a field characterized by “colored noise,” whose correlation function is different from that of the white noise field. In this approximation, the problem of a magnetoexciton in isolated and coupled quantum dots is considered. In the coherent-potential approximation, the exciton absorption in random fields of the first and second type in single and coupled quantum wells has been calculated. The absorption decreases as H increases in the range of strong magnetic fields, which is in agreement with experimental data. Zh. éksp. Teor. Fiz. 114, 1451–1465 (October 1998)     

On the properties of small-world network models

We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. [0.5cm] Received 29 March 1999 and Received in final form 21 May 1999     

Two-particle correlations in 1D-lattice systems with δ-interactions

The problem of two interacting particles in finite closed and open chains is solved by the Lifshitz method. The “density-density” correlation function, the dependence of the “surface” energy on the two-particle interaction energy and number of links in the chain, and the two-particle distribution on the chain are found and the nature of the ground state is clarified. Fiz. Tverd. Tela (St. Petersburg) 40, 366–370 (February 1998)     

Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem

The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics. PACS: 03.65.Ud, 04.60.Nc     

Diffusion of excitons in CdS-Se and ZnSe-Te solid solutions at high excitation levels

It is shown that, with strong pulsed excitation, the intensity of the exciton recombination band in the fluctuation tail of the density of states in the limit of large times in the presence of traps is described by the asymptote of a solution to the diffusion equation. The critical diffusion index corresponds to a “normal” process in the CdS-Se solid solution and to “anomalous” diffusion in the case of ZnSe-Te. Fiz. Tverd. Tela (St. Petersburg) 40, 892–893 (May 1998)     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Phase diagram of a 2D metal system with a variable number of carriers

It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 170–175 (25 January 1997)     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

Lorentz gas interacting with an inhomogeneous thermostat

The equilibrium distribution of a Lorentz gas (“electrons”) interacting with an inhomogenous thermostat (“atoms”) is examined with consideration of 1) the concept of volumes available and forbidden for the gas particles and 2) the solution of the kinetic equation. Analytical calculations for “electrons” and “atoms” repelling each other with the force ≈r⁻⁵ (where r is the distance between the particles) have shown that the coordinate- and velocity-dependent variables in the distribution function cannot be separated. In particular, this leads to the dependence of the average kinetic energy per “electron” on the coordinate: it is higher in the region with higher density of the “atoms”. It is assumed that the Gibbs distribution does not describe the properties of the system under consideration, because in this case the interaction between the system and thermostat cannot be considered small. Scientific-Research Physical-Technical Institute at N. I. Lobachevskii Nizhnii Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–43, June, 1999.     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

Relaxation processes in the incommensurate phase of a crystal with defects

The nature of the relaxation of the incommensurate superstructure of a ferroelectric to the equilibrium state is investigated experimentally. It is shown that near a phase transition the temperature dependence of the relaxation time of the incommensurate phase of the defective crystal is exponential. This law agrees qualitatively with the notion of domain wall motion in an inhomogeneous medium containing “random local phase-transition temperature” type defects. Fiz. Tverd. Tela (St. Petersburg) 41, 513–515 (March 1999)     

Role of electron “lakes” in the negative magnetoresistance effect in the region of Mott hopping conductivity

It is shown for doped and compensated germanium that the appearance of negative magnetoresistance under the conditions of Mott hopping conductivity may be due to the presence of a nonuniform spatial distribution of the electron density, the temperature at which the effect appears apparently being determined by the temperature at which the electron gas condenses into electron “lakes.” A “dead zone” effect was also observed in weak magnetic fields, the threshold field increasing with the nonuniformity of the electron distribution. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 187–191 (10 February 1996)     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.” Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999)     

Correlated Knowledge: an Epistemic-Logic View on Quantum Entanglement

In this paper we give a logical analysis of both classical and quantum correlations. We propose a new logical system to reason about the information carried by a complex system composed of several parts. Our formalism is based on an extension of epistemic logic with operators for “group knowledge” (the logic GEL), further extended with atomic sentences describing the results of “joint observations” (the logic LCK). As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models. We give sound and complete axiomatizations for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts of a complex system and the information carried by the whole system. In particular we distinguish between the “distributed information”, obtainable by simply pooling together all the information that can be separately observed in any of the parts, and “correlated information”, obtainable only by doing joint observations of the parts (and pooling together the results). Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical characterization of the notion of “quantum entanglement”.     

On the static permittivity of the Coulomb system in the long-wavelength limit

The general expression for the static permittivity ε(q, 0) of the Coulomb system in the region of small wave vectors was derived based on exact limit relations. The relation obtained describes the function ε(q, 0) in both “metal” and “dielectric” states of the Coulomb system. On this basis, the concept of the “true” dielectric is introduced and the definition of the “true” screening length was discussed. Exact relations were derived for the function ε(q, 0) in the region of small wave vectors q within the random phase approximation at an arbitrary degeneracy.     

On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function of the characteristic polynomial. Furthermore, we show that the second-order correlation function of the characteristic polynomial is closely related to that of the permanental polynomial. Supported by CRC 701 “Spectral Structures and Topological Methods in Mathematics”.     

“Non-Gibbsian” States and their Gibbs Description

The driving principle behind this paper is the following thesis: “Every physically reasonable random field has to be a Gibbs random field”. In this paper the so-called “non-Gibbsian” random fields are considered. The usual definition of the Gibbs field is generalized in such a way so as to include some of the discovered “non-Gibbsian” fields. The new definition is then used to show that the projection of the two-dimensional Ising model onto the one-dimensional sublattice ℤ¹ falls into the class of the generalized Gibbs fields. Received: 13 March 1998 / Accepted: 19 June 1998     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001