Quasi-Bound States of Two Magnons in the Spin-1/2XXZ Chain

We study two-magnon Bethe states in the spin-1/2 XXZ chain. The string hypothesis assumes that complex rapidities of the bound states take special forms. It is known, however, that there exist “non-string states,” which substantially disagrees with the string hypothesis. In order to clarify their nature, we study the large-N behavior of solutions of the Bethe-Ansatz equations to obtain explicit forms of typical Bethe states, where N is the length of the chain, and apply the scaling analysis (the multifractal analysis) to the Bethe states. It turns out that the non-string states contain “quasi-bound” states, which in some sense continuously interpolate between extended states and localized states. The “quasi-bound” states can be distinguished from known three types of states, i.e., extended, localized, and critical states. Our results indicate that there might be a need to reconsider the standard classification scheme of wavefunctions.     

Localized states in InxGa1−xN epitaxial film

This study investigated localized states from In_0.36Ga_0.64N epitaxial film grown on a Si (111) substrate by performing macro-photoluminescence, micro-photoluminescence and time-resolved micro-photoluminescence experiments. Experimental data revealed two localized states — single and extended. The single localized state is a single-quantum-dot-like deep confined energy state, which is responsible for the bright line emissions. The extended localized state is a shallow confined energy state, which is related to a broad background emission. This work suggests that the origin of single and extended localized states is the indium-rich In_xGa_1?xN cluster and the spatial indium concentration fluctuation, respectively.     

Picosecond time-resolved luminescence of localized excitons in CdS1-xSex

We present time-resolved luminescence results on CdS_0.36Se_0.64 which give a new insight on the kinetics of excitons localized by alloy potential fluctuations. By exciting in the localized exciton band with detection close to the exciting wavelength we obtain the lifetime across the band. Below the exciting laser energy two processes contribute to luminescence: transfer of localized excitons by tunnel effect assisted by acoustical phonons, and luminescence (assisted by acoustical phonons) of all the states excited at time t = 0 either directly or through their acoustical absorption wing. The time behavior of luminescence with respect to the detuning from the exciting energy helps to discriminate between those two contributions. Furthermore it shows that intermediate long-living states are involved in the exciton relaxation process.     

Superconductivity in impurity bands

We present a theory of superconductivity in doped insulators. In the magnetic metal state of the compound we obtain the self-consistency equations for the superconducting state in the spin-dependent impurity bands of both extended and localized states in the initial insulator gap. A BCS-type triplet pairing field is considered. We show that the superconducting gap in which single-electron extended states do not exist is overlapped by the distribution of the localized states. The formation of a latent superconducting gap is discussed in connection with the unusual properties of high-T _c compounds. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 419–424 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fractional Ornstein-Uhlenbeck processes. Joseph effect in models with infinite variance

We consider five fractional generalizations of the Markovian α-stable Ornstein-Uhlenbeck process and explore the dependence structure of these stochastic models. Since the variance of α-stable distributed random variables is infinite, we describe the dependence structure of the introduced processes in the language of the function called codifference. We present exact formulas for the asymptotic behavior of codifference and answer the question of long-range dependence property (Joseph effect) for the discussed fractional α-stable models. We show that the fractional Ornstein-Uhlenbeck processes can display both Noah and Joseph effect.     

Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

In this work we study the behavior of the allowed and forbidden frequencies in disordered classical dual transmission lines when the values of capacitances {Cj} are distributed according to a ternary model with long-range correlated disorder. We introduce the disorder from a random sequence with a power spectrum S(k)∝k−(2α−1), where α?0.5 is the correlation exponent. From this sequence we generate an asymmetric ternary map using two map parameters b₁ and b₂, which adjust the occupancy probability of each possible value of the capacitances Cj={CA,CB,CC,}. If the sequence of capacitance values is totally at random α=0.5 (white noise), the electrical transmission line is in the non-conducting state for every frequency ω. When we introduce long-range correlations in the distribution of capacitances, the electrical transmission lines can change their conducting properties and we can find a transition from the non-conducting to conducting state for a fixed system size. This implies the existence of critical values of the map parameters for each correlation exponent α. By performing finite-size scaling we obtain the asymptotic value of the map parameters in the thermodynamic limit for any α. With these data we obtain a phase diagram for the symmetric ternary model, which separates the non-conducting state from the conducting one. This is the fundamental result of this Letter. In addition, introducing one or more impurities in random places of the long-range correlated distribution of capacitances, we observe a dramatic change in the conducting properties of the electrical transmission lines, in such a way that the system jumps from conducting to non-conducting states. We think that this behavior can be considered as a possible mechanism to secure communication.     

Time-dependent mean field S-matrix theory

By using the path integral approach to many-body systems, we formulate a time-dependent mean field S-matrix theory of nuclear reactions. Many-body channel eigenstates are constructed by using projection techniques. In this way the S-matrix between the channel eigenstates is expressed as a superposition of S-matrix elements between wave-packet-like states localized in space and time. A field operator representation of the interaction picture S-matrix is derived which enables one to apply the path integral approach. Applying the stationary phase approximation to the path integral representation of the interaction picture S-matrix between the localized states an asymptotically constant time-dependent mean field approximation to this S-matrix is obtained. Finally, the S-matrix between the projected channel eigenstates is obtained by evaluating the integral, arising from the projections, over the space-time positions of the localized states in the stationary phase approximation. The stationary phase conditions select those localized states from the projected channel states for which the mean field values of energy and momentum coincide with their corresponding channel eigenvalues.     

Asymptotic dynamics,non-critical and critical fluctuations for a geometric long-range interacting model

We study the dynamics of geometric spin system on the torus with long-range interaction. As the number of particles goes to infinity, the process converges to a deterministic, dynamical magnetization field that satisfies an Euler equation (law of large numbers). Its stable steady states are related to the limits of the equilibrium measures (Gibbs states) of the finite particle system. A related equation holds for the magnetization densities, for which the property of propagation of chaos also is established. We prove a dynamical central limit theorem with an infinite-dimensional Ornstein-Uhlenbeck process as a limiting fluctuation process. At the critical temperature of a ferromagnetic phase transition, both a tighter quantity scaling and a time scaling is required to obtain convergence to a one-dimensional critical fluctuation process with constant magnetization fields, which has a non-Gaussian invariant distribution. Similarly, at the phase transition to an antiferromagnetic state with frequencyp ₀, the fluctuation process with critical scaling converges to a two-dimensional critical fluctuation process, which consists of fields with frequencyp ₀ and has a non-Gaussian invariant distribution on these fields. Finally, we compute the critical fluctuation process in the infinite particle limit at a triple point, where a ferromagnetic and an antiferromagnetic phase transition coincide.Work supported by Deutsche Forschungsgemeinschaft     

Why localized and extended impurity band states can coexist and be separated

It has been assumed that in the impurity band metallic regime there exists an energy E_c below which all states are localized and above which all states are extended. This discontinuous model contradicts the results of recent experiments. Using the quantum theory of measurement I resolve these difficulties as my title indicates.     

Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V _c , and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < V _c and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy E _c±, which separate the robustly delocalized states from “almost localized” states. We find that, besides E _c±, there exist additionally another energy edges E _c′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |E _c±|?≤?|E|?≤?|E _c′±| with the mobility edges E _c± and E _c′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > V _c , for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.     

Optimizing Spatially Localized NMR

Fourier-series windowing, a technique used to obtain spatially localized in vivo NMR spectra, is extended to fields-of-view containing a number of arbitrarily shaped regions of interest. For each volume, k-space weighting functions are derived and then combined to give an overall k-space sampling pattern - the number of signal acquisitions per phase-encoding vector - which can then be used to obtain spatially localized spectra of optimal sensitivity, consistent with a specified degree of localization. The technique is compared with the related methods of chemical-shift imaging and spectral localization by imaging.     

Diffusive, super-diffusive and ballistic transport in the long-range correlated 1D Anderson model

In this paper, we study the 1D Anderson model with long-range correlated on-site energies. This diagonal-correlated disorder is considered in such a way that the random sequence of site energies ε_n has a 1/k^α power spectrum, where k is the wave-vector of the modulations on the random sequence landscape. Using the Runge-Kutta method to solve the time-dependent Schrödinger equation, we compute the participation number and the Shannon entropy for an initially localized wave packet. We observe that strong correlations can induce ballistic transport associated with the emergence of low-energy extended states, in agreement with previous works in this model. We further identify an intermediate regime with super-diffusive spreading of the wave-packet.     

Relaxation dynamics of Mn2+ intraion excitation in Cd0.5Mn0.5Te: Dependence on the optical pumping level

A study is reported of the Mn²⁺ intracenter 3d luminescence in a dilute Cd_0.5Mn_0.5Te magnetic semiconductor at pulsed excitations of up to 3.5 MW/cm². At high excitation levels and at a temperature of 77 K, the kinetics varies strongly over the emission band profile. The luminescence decay curve can be resolved into a fast and a delayed component, which correspond to the excitation of extended and localized states in the manganese ion system. The fast relaxation of the extended states is largely determined by the up-conversion. As the temperature is lowered, the contribution of the fast component at the center of the emission band and in its low-energy wing decreases because of the weakening role of the extended states lying above the mobility edge.     

Re-localization due to finite response times in a nonlinear Anderson chain

We study a disordered nonlinear Schr?dinger equation with an additional relaxation process having a finite response time ??. Without the relaxation term, ?? = 0, this model has been widely studied in the past and numerical simulations showed subdiffusive spreading of initially localized excitations. However, recently Caetano et al. [Eur. Phys. J. B 80, 321 (2011)] found that by introducing a response time ?? > 0, spreading is suppressed and any initially localized excitation will remain localized. Here, we explain the lack of subdiffusive spreading for ?? > 0 by numerically analyzing the energy evolution. We find that in the presence of a relaxation process the energy drifts towards the band edge, which enforces the population of fewer and fewer localized modes and hence leads to re-localization. The explanation presented here relies on former findings by Mulansky et al. [Phys. Rev. E 80, 056212 (2009)] on the energy dependence of thermalized states.     

Valence,electronic specific heat and magnetic susceptibility of alpha-cerium

A sixfold degenerate Anderson Hamiltonian, which includes the Coulomb repulsion between localized and band states in the mean field approximation following Ramírez and Falicov, is treated in the limit of infinitely correlated 4? states and to second order in the mixing parameter. Assuming a line width Γ ≈ 0.02eV we obtain at low temperatures and 11 kbar, a valency of 3.76 and sizeable contributions from the 4? levels to the electronic specific heat and magnetic susceptibility of alpha Ce. Thus we show, that the highly correlated picture necessary to the explanation of the alpha—gamma transition by Ramírez and Falicov needs not to be abandoned in order to explain the anomalies in alpha Ce.     

Scanning tunneling microscopy of the nonequilibrium interaction of impurity states at semiconductor surfaces

Interaction of two localized impurity states of Si atoms at a GaAs surface was studied by scanning tunneling microscopy and spectroscopy. The effects of a twofold “switching” on and off of the states of each of the interacting atoms, the tunneling-interaction-induced mutual level pulling of these states, and the level stabilization near E _F were observed. These effects are explained in terms of the extended Anderson model.     

Character of the map for switched dynamical systems for observations on the switching manifold

It has been proposed to obtain the discrete-time models of switching dynamical systems by observing the states at the switching instants. Apart from the lowering of dimension, such switching maps or impact maps offer advantage in modeling systems that exhibit chattering. In this Letter we derive the nature of the switching map for the special case of grazing orbits. We show that the map is discontinuous in the neighborhood of a grazing orbit, and that it has a square root slope singularity on one side of the discontinuity. We illustrate the above by obtaining the switching maps for two example systems: the Colpitt's oscillator in the electrical domain and the soft impact oscillator in the mechanical domain.     

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge

Recently, an interesting family of quasiperiodic models with exact mobility edges(MEs) has been proposed(Phys.Rev. Lett. 114 146601(2015)). It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended(localized) states in the real space to localized(extended) ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.     

Optical and electrical properties of amorphous arsenic

Amorphous arsenic prepared by plasma decomposition of arsine has been characterized using field-effect conductance, thermopower, optical absorption, and photoconductivity measurements. It is found that the Fermi level is located in a density of states ～ 10¹⁷ cm^?3 eV^?1 approximately in the center of the forbidden gap, that conduction occurs via electrons in extended states in the conduction band, and that the optical and photoelectrical properties are very similar to those of bulk a-As. It is concluded that a model involving a negative correlation energy for localized states is inappropriate for this material.     

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Received: 7 July 2003, Published online: 19 November 2003PACS: 63.50. + x Vibrational states in disordered systems - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 62.30. + d Mechanical and elastic waves; vibrations