Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Phase control of maximal atomic coherence

The atomic coherence in a three-level Λ atom is studied, in which each optical transition is driven by a coherent field and the metastable states are coupled to each other via a microwave field. It’s shown that the atomic coherence crucially depends on the relative phase delay between the envelopes of the amplitudes of the three coupling fields. In particular, when the phase delay is adjusted to 0 or π, the maximal atomic coherence arises, while the maximal atomic coherence doesn’t occur once the phase delay is changed to π/2. The maximal atomic coherence is attributed to the trapping of the population in the lower sublevels.     

Interferometry with independent Bose-Einstein condensates: parity as an EPR/Bell quantum variable

When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results ±1. With two interferometers and two BEC’s, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number N of particles increases, and can therefore be obtained with arbitrarily large systems, but a condition is that all particles should be detected. We discuss the general experimental requirements for observing such effects, the necessary detection of all particles in correlation, the role of the pixels of the CCD detectors, and that of the alignments of the interferometers in terms of matching of the wave fronts of the sources in the detection regions. Another scheme involving three interferometers and three BEC’s is discussed; it leads to Greenberger-Horne-Zeilinger (GHZ) sign contradictions, as in the usual GHZ case with three particles, but for an arbitrarily large number of them. Finally, generalizations of the Hardy impossibilities to an arbitrarily large number of particles are introduced. BEC’s provide a large versality for observing violations of local realism in a variety of experimental arrangements.     

Synchronization of multi-phase oscillators: an Axelrod-inspired model

Inspired by Axelrod’s model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction – which occurs between homologous phases – is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where any two oscillators can be synchronized in some of their phases, while their remain unsynchronized in the others.     

Controlled π-junctions in a T-shaped double quantum dot system

The π-junction transition of a T-shaped double quantum dot system is investigated theoretically by using the nonequilibrium Green’s function method. It is found that the π-junction transition can occur with increasing the spin-flip strength. Furthermore, the π-junction in the system can be controlled by tuning the system parameters, such as the two quantum dot energy levels and the interdot coupling. These controlled π-junction transitions are interpreted in the picture of current-carrying density of states. When the main contributions to supercurrent is changed between the positive discrete spectrum and the negative continuous spectrum, the π-junction transitions can happen.     

Charging ratchets: Coulomb blockade and rectification

Discrete ratchets describe directed motion of a ‘reaction coordinate’ through a cycle of states in response to some varying external parameter. Such systems, in the simple, history-independent case, are described by a Markov process which in turn leads to a master equation with a transition matrix. Thus the ratchet property is reduced to a characteristic of the parameter-dependent symmetry of matrices. In the standard model of tunneling through a set of quantum dots in the Coulomb-blockade regime, a master equation is also used to describe the evolution through states in ‘dot-occupancy space’, leading to transport of electrons from a source to a drain. The symmetry of the transition matrix in this case is also a function of external parameters, notably the applied gate voltages and source–drain voltage, as well as depending on the configuration of dots and their tunnel couplings. We show that rectification and other ratchet behavior is a common feature of tunneling transport in the Coulomb-blockade regime. We also show that specific arrangements of dots and their tunnel couplings can be designed to enhance the ratchet effect. Finally, we show that the strong rectification of Coulomb-blockaded systems results from the reduction in phase space accessible to the system as it traverses the states in the reaction cycle. Received: 16 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Benford’s law and half-lives of unstable nuclei

We find that the experimental data of the -decay half-lives for 627 nuclei are in good agreement with Benford’s law, which states that the frequency of the appearance of each figure, 1-9, as the first significant digit, follows a logarithmic distribution favoring the smallest value. In order to generalize the applicability of Benford’s law, we systematically investigate the data of the total half-lives for 3177 nuclides in their ground and isomeric states, where the half-lives of many nuclei are determined by -decay and spontaneous fission. We find that they are also in excellent agreement with Benford’s law, although they are determined by different interactions such as strong, weak and electromagnetic interactions. The possible physics behind them is discussed. Moreover, Benford’s law can be used to test theoretical models or methods.     

Quasi-Diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

We study a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. Correlations in this model may be described in terms of a random walk in a highly correlated random environment. We prove that in three or more dimensions the model has a ‘diffusive’ phase at low temperatures. Localization is expected at high temperatures. Our analysis uses estimates on non-uniformly elliptic Green’s functions and a family of Ward identities coming from internal supersymmetry.     

Asymptotic results for a persistent diffusion model of Taylor dispersion of particles

We study Taylor diffusion for the case when the diffusion transverse to the bulk motion is a persistent random walk on a one-dimensional lattice. This is mapped onto a Markovian walk where each lattice site has two internal states. For such a model we find the effective diffusion coefficient which depends on the rate of transition among internal states of the lattice. The Markovian limit is recovered in the limit of infinite rate of transitions among internal states; the initial conditions have no role in the leading-order time-dependent term of the effective dispersion, but a strong effect on the constant term. We derive a continuum limit of the problem presented and study the asymptotic behavior of such limit.     

Study on composite photonic crystal patch antenna

The paper investigated a composite photonic crystal patch antenna by using the method of finite difference time domain (FDTD). The results show that there exists a wave resonance state at 2.635 GHz, where the real part of the permittivity and permeability are all negative; its refraction index is –1. The effect has largely enhanced the electromagnetic wave’s resonance intensity, and has improved the localized extent of electromagnetic energy obviously in such photonic crystal structure (PBG), resulting in a higher antenna gain, a lower return loss, and a better improvement of the antenna’s characteristics. Due to such the advantages, the use of patch antennas can be extended to such fields as mobile communication, satellite communication, aviation, etc.     

Phase transition and random-field induced domain wall response of SrTi O 3

The dielectric permittivity ε^′ - i of SrTi ¹⁸O ₃ (STO18) is studied under a dc electric field E as a function of the temperature, T. In ε^′ vs. T, a double-peak is found when 0 < E < 30 KV/m. While the peak at high-T is attributed to the smeared ferroelectric phase transition, the low-T one is induced by domain wall motion. The transverse Ising model including an external homogeneous and quenched random-fields is successfully used to describe both the smeared phase transition and the domain wall response in the low-T domain state. The calculations are in good agreement with the experimental results. Received 4 January 2002 / Received in final form 25 March 2002 Published online 19 July 2002     

The effects of time delay on the decline and propagation processes of population in the Malthus-Verhulst model with cross-correlated noises

This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring, using a Fokker-Planck formalism. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton’s law of “actio = reactio” and (ii) asymmetric, forwardly directed interactions as, for example in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions for asymmetric interactions and driving terms agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. This analytical result is confirmed by computer simulations and establishes the possibility of approximating the steady state statistics in driven many-particle systems by Hamiltonian systems. Our finding is also useful to understand the various departure time distributions of queueing systems as a possible effect of interactions among the elements in the respective queue [Physica A 363, 62 (2006)].     

Negative differential resistance in a one-dimensional molecular wire with odd number of atoms

We have investigated the effects of electron-phonon coupling on the current-voltage characteristics of a one-dimensional molecular wire with odd number of atoms. The wire has been modelled using the Su-Schreiffer-Heeger (SSH) Hamiltonian and the current-voltage characteristics have been obtained using the Landauer’s formalism. In the presence of strong electron-lattice coupling, we find that there are regions of negative differential resistance (NDR) at some critical bias, due to the degeneracy in the energies of the frontier molecular orbitals. The presence of the applied bias and the electron-lattice coupling results in the delocalization of these low-lying molecular states leading to the NDR behaviour.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

Polymers with self-avoiding interaction in random medium: a localization-delocalization transition

In this paper we investigate the problem of a long self-avoiding polymer chain immersed in a random medium. We find that in the limit of a very long chain and when the self-avoiding interaction is weak, the conformation of the chain consists of many “blobs” with connecting segments. The blobs are sections of the molecule curled up in regions of low potential in the case of a Gaussian distributed random potential or in regions of relatively low density of obstacles in the case of randomly distributed hard obstacles. We find that as the strength of the self-avoiding interaction is increased the chain undergoes a delocalization transition in the sense that the appropriate free energy per monomer is no longer negative. The chain is then no longer bound to a particular location in the medium but can easily wander around under the influence of a small perturbation. For a localized chain we estimate quantitatively the expected number of monomers in the “blobs” and in the connecting segments. Received 13 November 2002 Published online 14 March 2003     

Pinning of cracks in two-dimensional disordered media

We study the statistics of crack pinning in two dimensions by experiments and simulations of directed polymers in random media. Mode I tensile tests on paper samples show a delocalization phenomenon as the notch length is varied if the fraction of cracks pinned to the notch is monitored. This is compared with the behavior of directed polymers in the presence of both an energetically favorable localized pinning center and bulk disorder. An analysis of the crack interface roughness indicates self-affine behavior with a roughness exponent ζ in the proximity of the minimum energy surface value 2/3. Received 4 April 2000 and Received in final form 10 October 2000     

Phase-field study of free growth in a channel: from thermal to chemical solidification

The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green’s function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.     

Some comments on the Coriolis attenuation problem

To explore the Coriolis attenuation problem we have carried out a schematici _13/2 rotor plus single quasi-particle band-mixing calculation. The results reveal that the calculations are largely insensitive towards the location of the Fermi energy near the low-K single particle states only, and therefore are incapable of taking into account the transition from ‘full’ decoupling to ‘partial’ decoupling as the Fermi level is increased. We trace the possible reasons for this insensitivity and find that this may be primarily due to thebcs approximation for calculating the quasiparticle energies.