The oxygen isotope effect on critical temperature in superconducting copper oxides

The isotope effect provided a crucial key to the development of the BCS (Bardeen-Cooper-Schrieffer) microscopic theory of superconductivity for conventional superconductors. In superconducting cooper oxides (cuprates) showing an unconventional type of superconductivity, the oxygen isotope effect is very peculiar: the exponential coefficient strongly depends on doping level. No consensus has been reached so far on the origin of the isotope effect in the cuprates. Here we show that the oxygen isotope effect in cuprates is in agreement with the bisoliton theory of superconductivity.Comment: 3 pages including 4 figures; version 2 is with minor correction

Influence of the sign of the coupling on the temperature dependence of optical properties of one-dimensional exciton models

A new physical cause for a temperature-dependent double peak in exciton systems is put forward within a thermal equilibrium approach for the calculation of optical properties of exciton systems. Indeed, it is found that one-dimensional exciton systems with only one molecule per unit cell can have an absorption spectrum characterized by a double peak provided that the coupling between excitations in different molecules is positive. The two peaks, whose relative intensities vary with temperature, are located around the exciton band edges, being separated by an energy of approximately 4V, where V is the average coupling between nearest neighbours. For small amounts of diagonal and off-diagonal disorder, the contributions from the intermediate states in the band are also visible as intermediate structure between the two peaks, this being enhanced for systems with periodic boundary conditions. At a qualitative level, these results correlate well with experimental observations in the molecular aggregates of the thiacarbocyanine dye THIATS and in the organic crystals of acetanilide and N-methylacetamide

Phonon Coherence and New Set of Sidebands in Phonon-Assisted Photoluminescence

We investigate excitonic polaron states comprising a local exciton and phonons in the longitudinal optical (LO) mode by solving the Schr\"{o}dinger equation. We derive an exact expression for the ground state (GS), which includes multi-phonon components with coefficients satisfying the Huang-Rhys factors. The recombination of GS and excited polaron states gives one set of sidebands in photoluminescence (PL): the multi-phonon components in the GS produce the Stokes lines and the zero-phonon components in the excited states produce the anti-Stokes lines. By introducing the mixing of the LO mode and environal phonon modes, the exciton will also couple with the latter, and the resultant polaron states result in another set of phonon sidebands. This set has a zero-phonon line higher and wider than that of the first set due to the tremendous number of the environal modes. The energy spacing between the zero-phonon lines of the first and second sets is proved to be the binding energy of the GS state. The common exciton origin of these two sets can be further verified by a characteristic Fano lineshape induced by the coherence in the mixing of the LO and the environal modes.Comment: 5 pages, 3 figures 1 figure (fig. 1) replaced 1 figure (fig. 2) remove

WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

Separation of the Dirac equation in the spacetime around a Kerr black hole into radial and angular coordinates was done by Chandrasekhar in 1976. In the present paper, we solve the radial equations in a Schwarzschild geometry semi-analytically using Wentzel-Kramers-Brillouin approximation (in short WKB) method. Among other things, we present analytical expression of the instantaneous reflection and transmission coefficients and the radial wave functions of the Dirac particles. Complete physical parameter space was divided into two parts depending on the height of the potential well and energy of the incoming waves. We show the general solution for these two regions. We also solve the equations by a Quantum Mechanical approach, in which the potential is approximated by a series of steps and found that these two solutions agree. We compare solutions of different initial parameters and show how the properties of the scattered wave depend on these parameters.Comment: RevTex, 11 Latex pages and 12 Figures ; Classical and Quantum Gravity (in Press) (1999

Surface solitons in quasiperiodic nonlinear photonic lattices

We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-Andr\'e types, and explore different families of localized surface modes, as a function of optical power content (`nonlinearity') and quasiperiodic strength (`disorder'). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focussing and defocussing nonlinearity, in both models. We also examine the dynamical evolution of a completely-localized initial excitation at the array surface. We find that in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk.Comment: 8 pages, 7 figures, submitted for publicatio

Exciton-Polariton scattering for defect detection in cold atom Optical Lattices

We study the effect of defects in the Mott insulator phase of ultracold atoms in an optical lattice on the dynamics of resonant excitations. Defects, which can either be empty sites in a Mott insulator state with one atom per site or a singly occupied site for a filling factor two, change the dynamics of Frenkel excitons and cavity polaritons. While the vacancies in first case behave like hard sphere scatters for excitons, singly occupied sites in the latter case can lead to attractive or repulsive scattering potentials. We suggest cavity polaritons as observation tool of such defects, and show how the scattering can be controlled in changing the exciton-photon detuning. In the case of asymmetric optical lattice sites we present how the scattering effective potential can be detuned by the cavity photon polarization direction, with the possibility of a crossover from a repulsive into an attractive potential.Comment: 9 pages, 10 figure

The string model of the Cooper pair in the anisotropic superconductor

The analogy between the Cooper pair in high temperature superconductor and the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD the nonlinear chromodynamical field between a quark and an antiquark is confined to a tube. So we assume that there is the strong interaction between phonons which can confine them to some tube too. This tube is described using the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum of axially symmetric (string) solutions with negative finite linear energy density. The one-dimensional nonlinear Schr\"odinger equation has a finite spectrum (hence, it has a steady-state) which describes the Cooper pair squezeed between anisotropy planes in the superconductor. It is shown that in this model the transition temperature is approximately 45 K.Comment: final version, Latex, 9p, to be published in Phys. Rev.

Quantum coherence and carriers mobility in organic semiconductors

We present a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier. Thermal intermolecular phonons and librations tend to localize pure coherent states and to assist the motion of less coherent ones. Decoherence is thus the primary mechanism by which conduction occurs. It is driven by the coupling of the carrier to the molecular lattice through polarization and transfer integral fluctuations as described by the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent regime are modeled via the Anderson hamiltonian with correlated diagonal and non-diagonal disorder leading to the determination of the carrier localization length. This length defines the coherent extension of the ground state and determines, in turn, the diffusion range in the incoherent regime and thus the mobility. The transfer integral disorder of Troisi and Orlandi can also be incorporated. This model, based on the idea of decoherence, allowed us to predict the value and temperature dependence of the carrier mobility in prototypical organic semiconductors that are in qualitative accord with experiments

Extension of Frohlich's method to 4-fermion interactions

Higher order terms of the transformed electron-phonon Hamiltonian, obtained by performing the Frohlich's transformation, are investigated. The influence of terms discarded by Frohlich (in particular those proportional to the third power of electron-phonon coupling) on the effective Hamiltonian is examined. To this end a second Frohlich-type transformation is performed, which yields, among others, an effective 4-electron interaction. This interaction is reduced to a form admitting solution of thermodynamics. The form of the coupling of the 4-electron interaction is found. By applying standard approximations, it is shown that this interaction is attractive with interaction coupling given by - D_{k_F}^6 / \omega_{k_F}^5, where D_{k} is electron-phonon coupling, \omega_{k}$ is phonon energy and k_F is Fermi momentum. The form of higher order terms of the original Frohlich-transformed H_{e-ph} are also found, up to terms proportional to the 6-th power of the coupling, that is up to those, which yield the effective 4-electron interactions.Comment: REVTeX4, 25 pages; major changes: added section and appendix about the form of 4-fermion interaction coupling, typos correcte