We present nonlocal integrable reductions of the Fordy–Kulish system of nonlinear Schrodinger equations and the Fordy system of derivative nonlinear Schrodinger equations on Hermitian symmetric spaces. Examples are given on the symmetric space SU(4)SU(2)×SU(2).
We investigate the interplay between the spin interference and the Fano effect in a three-lead mesoscopic ring with a side-coupled quantum dot (QD). A uniform Rashba spin-orbit coupling and a perpendicular magnetic field are tuned such that the ring operates as a spin splitter in the absence of the QD: one lead is used to inject unpolarized electrons and the remaining (output) leads collect almost polarized spin currents. By applying a gate potential to the quantum dot a pair of spin-split levels sweeps the bias window and leads to Fano interference. The steady-state spin and charge currents in the leads are calculated for a finite bias applied across the ring via the non-equilibrium Greens function formalism. When the QD levels participate to transport we find that the spin currents exhibit peaks and dips whereas the charge currents present Fano lineshapes. The location of the side-coupled quantum dot and the spin splitting of its levels also affect the interference and the output currents. The opposite response of output currents to the variation of the gate potential allows one to use this system as a single parameter current switch. We also analyze the dependence of the splitter efficiency on the spin splitting on the QD.
We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form S-q equivalent to [1 - Sigma (W)(i=1) P-i(q)]/[q-1] (with S-1 equivalent to -Sigma (W)(i=1) pi ln pi) for two families of one-dimensional dissipative maps, namely a logistic-like and a generalized cosine with arbitrary inflexion z at their maximum. At t = 0 we choose N initial conditions inside one of the W small windows in which the accessible phase space is partitioned; to neutralize large fluctuations we conveniently average over a large amount of initial windows. We verify that one and only one value q* < 1 exists such that the lim(t --> infinity)limW(--> infinity) limN(--> infinity) S-q (t)/t is finite, thus generalizing the (ensemble version of the) Kolmogorov-Sinai entropy (which corresponds to q* = 1 in the present formalism). This special, z-dependent, value q* numerically coincides, for both families of maps and all z, with the one previously found through two other independent procedures (sensitivity to the initial conditions and multifractal 0 f (alpha) function). (C) 2001 Elsevier Science B.V. All rights reserved.
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Renyi and Tsallis entropies. The generalized entropy maximization procedure for Renyi entropies results in the exponential stationary distribution asymptotically for q is an element of (0, 1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure. (C) 2009 Elsevier B.V. All rights reserved.
By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1 <= q < 2, while the interval 0 < q <= 1 corresponds to any real argument greater than 1 (positive real numbers). These two distinct intervals of the nonextensivity index q, also the expressions of the deformed functions associated with them, are related to one another through the relation (2 - q), which is so far used to obtain the ordinary stationary distributions from the corresponding escort distributions. and vice versa in an almost ad hoc manner. This shows that the escort distributions are only a means of extending the interval of validity of the deformed functions to the one of ordinary, undeformed ones. Moreover, we show that, since the Tsallis entropy is written in terms of the q-logarithm and its argument, being the inverse of microstate probabilities, takes values equal to or greater than 1, the resulting stationary solution is uniquely described by the one obtained from the ordinary constraint. Finally, we observe that even the escort stationary distributions can be obtained through the use of the ordinary averaging procedure if the argument of the q-exponential lies in (-infinity, 0]. However, this case corresponds to, although related, a different entropy expression than the Tsallis entropy. (C) 2010 Elsevier B.V. All rights reserved.
In this Letter, we used homotopy perturbation method to obtain numerical solution of the 3D Greens function for the dynamic system of anisotropic elasticity. Application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results obtained from convolution of Greens function and data of the Cauchy problem are compared with the exact solution for cubic media. The results reveal that the proposed method is very effective and simple. (C) 2009 Elsevier B.V. All rights reserved.
The one-dimensional Dirac equation is solved for the PT-symmetric generalized Hulthen potential. The Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. (c) 2005 Elsevier B.V. All rights reserved.
The laser-field dependence of the binding energy of shallow-donor impurities in graded, and square quantum wells under the external magnetic field is calculated by a variational method and in the effective mass approximation. We have shown that, not only the dressed potential, but also the shape of the confinement potential, the strength of the external magnetic field parallel to the growth direction, and the impurity position play very important roles in the determining the binding energy of a hydrogenic impurity. (C) 2003 Elsevier Science B.V. All rights reserved.
We have investigated the dynamics of quantum discord and entanglement for two qubits subject to independent global transverse and/or longitudinal memoryless noisy classical fields. Global transverse and/or longitudinal random fields are found to drive the system to maximally discordant mixed separable steady states for suitable initial conditions. Moreover, two independent noises in the system are found to enhance both the steady state randomness and quantum discord in the absence of entanglement for some initial states. (C) 2012 Elsevier B.V. All rights reserved.
In this Letter, we study the exactly solvable generalized PT symmetric harmonic oscillator problem. Some transformations are introduced for this problem to make the potential time-dependent. PT symmetry and the reality of energy eigenvalues are studied under these transformations. (C) 2005 Elsevier B.V. All rights reserved.
We have investigated the ground-state and the thermal entanglement properties of a two-dimensional frustrated spin 1/2 cluster by calculating the pairwise concurrence and negativity. It is found that an increase in temperature can lead to an enhancement of pairwise entanglement for a certain range of the frustration parameter. We have, also, found that negativity is equal to the half of the concurrence for the model considered here. (c) 2006 Elsevier B.V. All rights reserved.
A new scheme, deduced from Hes homotopy perturbation method, is presented for solving Lane-Emden type singular IVPs problem. The scheme is shown to be highly accurate, and only a few terms are required to obtain accurate computable solutions. (C) 2007 Elsevier B.V. All rights reserved.
Peculiarities of the biphasic regions at the direct and reverse phase transitions between homeotropic oriented nematic mesophase and isotropic liquid have been investigated in detail in this work. The shift of phase transition temperatures to the low temperatures by the reverse phase transitions have been observed for this mesophase. Nonlinearity of thermotropic and thermo-optical properties at the phase transitions between nematic mesophase, and isotropic liquid have been found. (c) 2006 Elsevier B.V. All rights reserved.
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one. (C) 2015 Elsevier B.V. All rights reserved.
We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states. (c) 2010 Elsevier B.V. All rights reserved.
in this Letter, we present analytical and numerical solutions for an axis-symmetric diffusion-wave equation. For problem formulation. the fractional time derivative is described in the sense of Riemann-Liouville. The analytical solution of the problem is determined by using the method of separation of variables. Eigenfunctions whose linear combination constitute the closed form of the solution are obtained. For numerical computation, the fractional derivative is approximated using the Grunwald-Letnikov scheme. Simulation results are given for different values of order of fractional derivative. We indicate the effectiveness of numerical scheme by comparing the numerical and the analytical results for alpha = 1 which represents the order of derivative.