Scaling in the BCS to Bose crossover problem in different partial waves

The BCS superconductivity to Bose condensation crossover problem is studied in two dimensions in S, P, and D waves, for a simple anisotropic pairing, with a finite-range separable potential at zero temperature. The gap parameter and the chemical potential as a function of Cooper-pair binding B c exhibit universal scaling. In the BCS limit the results for coherence length ξ and the critical temperature T c are appropriate for highT c cuprate superconductors and also exhibit universal scaling as a function of B c.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Variational method for excited states from supersymmetric techniques

We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration.

Absence of Klein's paradox for massive spinless bosons coupled by a nonminimal vector interaction

A few properties of the nonminimal vector interaction in the Duffin-Kemmer-Petiau theory in the scalar sector are revised. In particular, it is shown that the nonminimal vector interaction has been erroneously applied to the description of elastic meson-nucleus scatterings and that the space component of the nonminimal vector interaction plays a peremptory role for the confinement of bosons whereas its time component contributes to the leakage. Scattering in a square step potential is used to show that Klein's paradox does not manifest in the case of a nonminimal vector coupling. Copyright © owned by the author(s) under the terms of the Creative Commons Attribution- NonCommercial-ShareAlike Licence.

O potêncial de poço duplo e a molécula de amônia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Screened potential and quarkonia properties at high temperatures

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Thermodynamics of quasi-particles at finite chemical potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Escape of particles in a time-dependent potential well

We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

Infrared finite gluon propagator and the structure of chiral symmetry breaking

We study the chiral symmetry breaking in QCD, using an effective potential for composite operators, with infrared finite gluon propagators that have been found by numerical calculation of the Schwinger-Dyson equations as well as in lattice simulations. The existence of a gluon propagator that is finite at k2 = 0 modifies substantially the transition between the phases with and without chiral symmetry.

Trapping of a particle in a short-range harmonic potential well

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed. © 2012 Springer Science+Business Media, LLC.

Study of the ℤ3 symmetry in QCD at finite temperature and chemical potential using a worm algorithm

Traditional Monte Carlo simulations of QCD in the presence of a baryon chemical potential are plagued by the complex phase problem and new numerical approaches are necessary for studying the phase diagram of the theory. In this work we consider a ℤ3 Polyakov loop model for the deconfining phase transition in QCD and discuss how a flux representation of the model in terms of dimer and monomer variable solves the complex action problem. We present results of numerical simulations using a worm algorithm for the specific heat and two-point correlation function of Polyakov loops. Evidences of a first order deconfinement phase transition are discussed. © 2013 American Institute of Physics.

Dynamical properties for an ensemble of classical particles moving in a driven potential well with different time perturbation

We consider dynamical properties for an ensemble of classical particles confined to an infinite box of potential and containing a time-dependent potential well described by different nonlinear functions. For smooth functions, the phase space contains chaotic trajectories, periodic islands and invariant spanning curves preventing the unlimited particle diffusion along the energy axis. Average properties of the chaotic sea are characterised as a function of the control parameters and exponents describing their behaviour show no dependence on the perturbation functions. Given invariant spanning curves are present in the phase space, a sticky region was observed and show to modify locally the diffusion of the particles. © 2013 Elsevier B.V.

Phase space properties and chaotic transport for a particle moving in a time dependent step potential well

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.