Entropic uncertainty measure for fluctuations in two-level electron-phonon models

Two-level electron-phonon systems with reflection symmetry linearly coupled to one or two phonon modes (exciton and E$\otimes(b_1+b_2)$ Jahn-Teller model) exhibit strong enhancement of quantum fluctuations of the phonon coordinates and momenta due to the complex interplay of quantum fluctuations and nonlinearities inherent to the models. We show that for the complex correlated quantum fluctuations of the anisotropic two-level systems the Shannon entropies of phonon coordinate and momentum and their sum yield their proper global description. On the other hand, the variance measures of the Heisenberg uncertainties suffer from several shortcomings to provide proper description of the fluctuations. Wave functions, related entropies and variances were determined by direct numerical simulations. Illustrative variational calculations were performed to demonstrate the effect on an analytically tractable exciton model.Comment: 14 pages, 10 figs, published in Eur.Phys.J 38 B (2004) 25-3

Nonadiabatic effects in a generalized Jahn-Teller lattice model: heavy and light polarons, pairing and metal-insulator transition

The ground state polaron potential of 1D lattice of two-level molecules with spinless electrons and two Einstein phonon modes with quantum phonon-assisted transitions between the levels is found anharmonic in phonon displacements. The potential shows a crossover from two nonequivalent broad minima to a single narrow minimum corresponding to the level positions in the ground state. Generalized variational approach implies prominent nonadiabatic effects:(i) In the limit of the symmetric E-e Jahn- Teller situation they cause transition between the regime of the predominantly one-level "heavy" polaron and a "light" polaron oscillating between the levels due to phonon assistance with almost vanishing polaron displacement. It implies enhancement of the electron transfer due to decrease of the "heavy" polaron mass (undressing) at the point of the transition. Pairing of "light" polarons due to exchange of virtual phonons occurs. Continuous transition to new energy ground state close to the transition from "heavy" polaron phase to "light" (bi)polaron phase occurs. In the "heavy" phase, there occurs anomalous (anharmonic) enhancements of quantum fluctuations of the phonon coordinate, momentum and their product as functions of the effective coupling. (ii) Dependence of the polaron mass on the optical phonon frequency appears.(iii) Rabi oscillations significantly enhance quantum shift of the insulator-metal transition line to higher values of the critical effective e-ph coupling supporting so the metallic phase. In the E-e JT case, insulator-metal transition coincide with the transition between the "heavy" and the "light" (bi)polaron phase at certain (strong) effective e-ph interaction.Comment: Paper in LaTex format (file jtseptx.tex) and 9 GIF-figures (ppic_1.gif,...ppic_9.gif

Creation of discrete solitons and observation of the Peierls-Nabarro barrier in Bose-Einstein Condensates

We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of 1D discrete solitons, for both attractive and repulsive interatomic interactions. We then address the issue of their mobility, focusing our attention on the conditions for the experimental observability of the Peierls-Nabarro barrier. Finally we report on the generation of self-trapped structures in two and three dimensions. Discrete solitons may open alternative routes for the manipulation and transport of Bose-Einstein condensates.Comment: 7 pages, 6 eps figure

Discrete localized modes supported by an inhomogeneous defocusing nonlinearity

We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form, and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying inter-site coupling is introduced and briefly considered too. Via a similar mechanism, it may also support UnST discrete solitons, under the action of the SDF nonlinearity. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered too.Comment: 14 pages, 7 figures, accepted for publication in PR

Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

On leaders and condensates in a growing network

The Bianconi-Barabasi model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fitnesses, has the fundamental property to undergo a phase transition to a condensed phase below some finite critical temperature, for an appropriate choice of the distribution of fitnesses. At high temperature it exhibits a crossover to the Barabasi-Albert model, and at low temperature, where the fitness landscape becomes very rugged, a crossover to the recently introduced record-driven growth process. We first present an analysis of the history of leaders, the leader being defined as the node with largest degree at a given time. In the generic finite-temperature regime, new leaders appear endlessly, albeit on a doubly logarithmic time scale, i.e., extremely slowly. We then give a novel picture for the dynamics in the condensed phase. The latter is characterized by an infinite hierarchy of condensates, whose sizes are non-self-averaging and keep fluctuating forever.Comment: 29 pages, 13 figures, 3 tables. A few minor change