Parity effects in eigenvalue correlators, parametric and crossover correlators in random matrix models: Application to mesoscopic systems

This paper summarizes some work that I have been doing on eigenvalue correlators of random matrix models which show some interesting behavior. First we consider matrix models with gaps in their spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the Hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems.     

Large‐Scale Fluctuation Behavior Prior to the Crystallization of Poly(ethylene terephthalate) Glass: A Small‐Angle Light Scattering Study

The crystallization processes of amorphous, glassy‐state poly(ethylene terephthalate) (PET) at two temperatures, a low temperature near T _g where PET has a slow crystallization speed and a middle temperature (about 55°C above T _g ) where PET crystallization is rapid, were monitored in situ by a time‐resolved small‐angle light scattering (SALS) device. It was found that large‐scale fluctuations happened prior to the crystallization at both temperatures, but the kind of fluctuation had a temperature dependence: at the middle temperature, pure density fluctuation took place during the induction period, whereas at low temperature, both density fluctuation and orientation fluctuation occurred, but the latter was the dominant factor. Analyses of the kinetics of these two kinds of fluctuation processes demonstrated that the spinodal decomposition (SD) type of phase‐separation character was undistinguishable in the SALS scale, while the nucleation‐growth (NG) type of phase behavior could describe the scattering results as well.     

Bistability,autowaves and dissipative structures in semiconductor fibers with anomalous resistivity properties

This work provides a discussion of bistability conditions, switching autowave properties and emergence of dissipative structures in semiconducting fibers with anomalous positive dependence of electrical resistivity on temperature of sigmoid type, (1?+?e ^?T )^?1. An open system thermodynamics approach is utilized for the analysis of this dissipative solid-state system. The approach aims to represent the structure of the solution space of its governing equation in the form of physical phase diagrams, known as non-equilibrium phase diagrams, and two specific binary diagrams have been obtained here. One of the diagrams, where the electrical power density and ambient temperature represent external parameters, shows a wide region with dissipative structures as non-uniform steady-state temperature profiles on the fiber. The possibility of efficient external control over the dissipative structure geometry is also demonstrated.     

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity () and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman’s system, which is described by the Lagrangian: which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting specifically for a dual extended damped–amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman’s Hamiltonian ?. The Heisenberg equations of motion utilizing the quantized Hamiltonian surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped–amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.     

Spacer layer thickness fluctuation scattering in a modulation-doped AlxGa1-xAs/GaAs/AlxGa1-xAs quantum well

We theoretically study the influence of spacer layer thickness fluctuation（SLTF） on the mobility of a twodimensional electron gas（2DEG） in the modulation-doped Al x Ga 1 x As/GaAs/Al x Ga 1 x As quantum well.The dependence of the mobility limited by SLTF scattering on spacer layer thickness and donor density are obtained.The results show that SLTF scattering is an important scattering mechanism for the quantum well structure with a thick well layer.     

Scattering Theory for Open Quantum Systems with Finite Rank Coupling

Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A _D in a Hilbert space \({\mathfrak H}\) is used to describe an open quantum system. In this case the minimal self-adjoint dilation \(\widetilde K\) of A _D can be regarded as the Hamiltonian of a closed system which contains the open system \(\{A_{\!D},{\mathfrak H}\}\), but since \(\widetilde K\) is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm–Liouville operators arising in dissipative and quantum transmitting Schrödinger–Poisson systems.     

Energy filtration of charge carriers in a nanostructured material based on bismuth telluride

The dependences of the electrical conductivity and thermopower on the size of grains in a nanocrystalline material based on Bi₂Te₃-Sb₂Te₃ solid solutions of the p type have been investigated theoretically and experimentally. The relaxation time in the case of hole scattering by nanograin boundaries in an isotropic polycrystal has been calculated taking into account the energy dependence of the probability of tunneling of charge carriers and the dependence of the scattering intensity on the nanograin size L _n . A decrease in the probability of boundary scattering with an increase in the energy of charge carriers leads to an increase in the thermopower. The dependences of the thermopower and electrical conductivity on the nanograin size, which have been obtained taking into account the boundary scattering and scattering by acoustic phonons, are in good agreement with experimental data. For the material under consideration, the thermopower coefficient increases by 10–20% compared to the initial solid solution at L _n = 20–30 nm. This can lead to an increase in the thermoelectric figure of merit by 20–40%, provided that the decrease in the electrical conductivity and the decrease in the lattice thermal conductivity compensate each other. Despite the absence of a complete compensation, it has been possible to increase the thermoelectric figure of merit for the samples under investigation to ZT = 1.10–1.12.     

Impurity Driven Linear and Nonlinear MHD Cylindrical Waves in a Three Species Plasma

The propagation of axisymmetric linear and nonlinear dispersive waves in a three species plasma to include the thermoelectrostatic effects together with the dissipative effects of main ions has been discussed. The impurity driven MHD fluid modes have been examined when the electrostatic drift has been taken into account. We have discussed the linear propagation of dispersive cylindrical waves in the plasma system for different ion thermal phase number. The thermal force resulting from the collisions between main ion and impurity ion densities (i.e. α_iI = 0) has been neglected. The shock waves and the soliton solutions are obtained for two different cases of the non-collisional plasma and the non-dissipative plasma.     

Electrical transport in La1−x Ca x MnO3 thin films at low temperatures

We report here the low-temperature resistivity of the chemical solution deposited La_1−x Ca _x MnO₃ (x=0.2, 0.3 and 0.33) thin films on LaAlO₃ substrates. The films were post-annealed in atmosphere at 850°C. The low temperature resistivity data has been studied in order to understand the nature of low-temperature conduction processes. The data showed T ² dependence from 60 K to 120 K consistent with the single magnon scattering process. The deviation from this quadratic temperature dependence at low temperatures is attributed to the collapse of the minority spin band. The two-magnon and electron-phonon processes contribute to scattering of carriers in the temperature range above 120 K.     

On the Present Status of the Problem of Charge Dependence and Charge Asymmetry of the Nucleon-Nucleon Force

The charge dependence of the nucleon-nucleon force can be derived from the low-energy scattering parameters. The p-p and n-p parameters were measured in direct scattering experiments. The n-n parameters a_nn = (-16.70 ± 0.38) fm and r_nn = (2.78 ± 0.13) fm have been determined from few particle reactions. The difference of the scattering lengths (a_nn - a_nn) ≈ 7 fm demonstrates the violation of the charge independence. Information on the charge symmetry is still doubtful due to the inaccuracy of the charge correction for the p-p parameters. Whereas the n-n and the charge corrected p-p parameters known at present yield a weaker n-n force than the p-p force, the opposite result follows from the binding energy difference for ³He and ³H and the meson theory of the nuclear forces.     

Perpendicular magnetic anisotropy in the Co50Pt50, Co50Pd50, and Co50Pt50 ? xPdx thin films

Films of the Co₅₀Pt₅₀, Co₅₀Pd₅₀, and Co₅₀Pt_{50 − x} Pd _x alloys (where x = 1–10 at %) have been prepared. The processes of atomic ordering and its influence on the perpendicular magnetic anisotropy and the coercive force in these films have been investigated. The dependence of the coercive force on the film thickness has been analyzed. It has been shown that thin films of ordered alloys become magnetically uniaxial with the easy axis normal to their plane and can be used for magnetic and thermomagnetic recording and storage of information.     

Magnetocrystalline symmetry, spin statics and dynamics in high-temperature superconductors

The symmetry analysis of the magnetic structures of La₂CuO₄ and YBa₂Cu₃O_6+δ (δ 0.4) antiferromagnetic oxide has been carried out. The spin configurations and spin-reorientation transition fields have been found. The frequencies of uniform spin oscillations and the external field dependence of their polarization properties have been calculated. It has been shown that the spin excitation branches may include exchange modes among which some dipole-active modes can be present. The spectrum of the inelastic light scattering accompanied with the excitation of spin and libration (tilting) freedom degrees has been discussed.     

Theoretical Treatment of Nonstationary Scattering by Phonons and Polaritons Part I. Derivation of the Basic Equations

The equations of motion of a two-level system and a harmonic oscillator coupled to a dissipative system are discussed; the dissipative system is assumed to consist of a large number of radiation oscillators. Special equations for the determination of the correlation functions of the fluctuation forces are derived under the condition of large time values, for which the atomic system has “forgotten” its initial state. The expectation values of the correlation functions are connected with the damping constant and the population operator of the excited state of the atomic system is in thermal equilibrium. Taking into account the influence of the coherent radiation field on the atomic system, the basic equations for the treatment of the nonstationary Raman scattering by polaritons are derived; the temporal range of validity is discussed. Using a time-dependent “variable” Fourier transformation, the nonstationary time- and spacedependent spectral densities are related to the correlation functions of the fields; here the Wiener-Khintchine theorem is applied in a nonstationary form. The limiting cases of the stationary scattering process as well as the usually introduced correlators of the slowly varying amplitudes are discussed.     

Transport properties in the pseudobinary (Gd,Y) Al2 series

The temperature dependence of the electrical resistivity, the thermal conductivity and the thermopower of the cubic isostructural (Gd_xY_1–x)Al₂ series will be presented. The magnetic properties of this system are characterized by the existence of ferromagnetism for Gd concentrations x>0.3 while for low Gd contents cluster and spinglass behaviour is observed. The spin dependent scattering contribution to the transport phenomena has been obtained by comparing the experimental data of the magnetic compounds with those of the isostructural nonmagnetic YAl₂. For the ferromagnetic concentration range and forT>T _c (T _c =Curie temperature) we revealed a temperature independent contribution to the electrical resistivity, a contribution with a temperature variation of 1/T to the thermal resistivity and a linear temperature dependence of this part to the thermopower. These results are in good agreement with the temperature dependence calculated by solving the linearized Boltzmann equation for this type of scattering processes.     

The c-Term of the Tucson-Melbourne Three-Body Force: To Be or Not to Be

 By Faddeev calculations of ³H we study the dependence of the binding energy on the three-nucleon force. We adopt the 2π-exchange Tucson-Melbourne three-nucleon force and investigate phenomenologically the dependence on the strength of the individual three-body force operators (the a-, b-, c-, and d-terms). While it is well known that the a-term is not as important as the b- and d-terms to gain the experimental binding energy, we find two solutions for the c-term, one around the value used in the original Tucson-Melbourne model and a new one close to zero. A tensor-analyzing power T ₂₀ of the pd elastic scattering using the modified Tucson-Melbourne model, which follows the recommendation by chiral perturbation theory that the short-range c-term should be dropped, describes the data well. Received April 22, 1999; revised June 6, 2000; accepted for publication June 16, 2000     

Paraconductivity for a d-wave superconductor in short-wavelength fluctuation regime

A theoretical study of the fluctuation conductivity above T_c (paraconductivity) is reported for a d-wave superconductor with resonant scattering impurities. A d-wave system is modeled by tight-binding electrons in the two-dimensional squared lattice, and the impurity scattering is treated in the T-matrix approximation in a unitary limit. In calculating the Aslamazov–Larkin (AL) and the Maki–Thompson (MT) terms, we also consider effects of a short-wavelength cutoff in the fluctuation spectrum. The d-wave character in the AL and MT terms manifests itself to renormalization effects on the fluctuation amplitude and reduced temperature, whereas an anomalous-MT term is absent. The present calculations can describe fairly well experiments on the paraconductivity in zinc-doped cuprate superconductors provided that effects of a total-energy cutoff are taken into account.     

Theoretical analysis on phase-locking properties of a laser diode array facing an external cavity

External coupling model has been used to describe the output field of a laser diode array (LDA) phase-locked with an external cavity. The analytical solution for the coupling matrix equation of the phase-locked system has been obtained. The dependencies of the threshold gain, g_j of the system mode on the residue reflection of the front facet, r_f and round trip external cavity lengths, L have been discussed. The working lengths of the external cavity for stably phase-locking the LDA of different residual reflectivities have been calculated.     

介观耗散电容耦合电路量子化中的正则变换

针对介观耗散电容耦合RLC电路提出一种一般的正则变换, 并证明了其正确性和合理性. 用这种正则变换研究了双回路介观耗散电容耦合电路的量子化问题, 得出的对角化哈密顿量比文献中多出一非线性项. 这种具有普遍性的一般正则变换可能对研究介观多回路耗散系统的量子涨落、量子噪声等性质具有重要的意义. 关键词： RLC电路')" href="#">RLC电路 量子化 正则变换     

Arrays of interacting ferromagnetic nanofilaments: Small-angle neutron diffraction study

Magnetic properties of spatially ordered arrays of interacting nanofilaments have been studied by means of small-angle diffraction of polarized neutrons. Several diffraction maxima or rings that correspond to the scattering of the highly ordered structure of pores/filaments with hexagonal packing have been observed in neutron scattering intensity maps. The interference (nuclear-magnetic) and pure magnetic contributions to the scattering have been analyzed during the magnetic reversal of the nanofilament array in a field applied perpendicular to the nanofilament axis. The average magnetization and the interference contribution proportional to it increase with the field and are saturated at H = H _S . The magnetic reversal process occurs almost without hysteresis. The intensity of the magnetic contribution has hysteresis behavior in the magnetic reversal process for both the positive and negative fields that form the field dependence of the intensity in a butterfly shape. It has been shown that this dependence is due to the magnetostatic interaction between the filaments in the field range of H ≤ H _S . A theory for describing the magnetic properties of the arrays of interacting ferromagnetic nanofilaments in the magnetic field has been proposed.     

Raman scattering from mixed crystals (HgBr2)1−x(HgI2)x

The behavior of long wavelength optic phonons in mixed system HgBr₂-HgI₂ has been investigated in Raman scattering. Different types of behavior, i.e. ‘persistent type’ and ‘amalgamation type’ were observed. Three strong Raman bands were observed for persistent type mode. These correspond to stretching vibration of HgBr₂, HgBrI, HgI₂ molecules. Intensity of these bands showed striking concentration dependence. A model based on nearly free molecular approximation have been proposed to explain the dependence. The analysis indicated that the distribution of anions on the sublattices is essentially random. For amalgamation (one-mode) type behavior, it is suggested that the intramolecular force relevant to the vibration is comparable to the intermolecular force and that the band width of the corresponding phonon branch in the parent crystal is broad enough to be degenerate with impurity mode at the low concentration limit.