The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

We study the Schrödinger equation with potentials admitting quasinormal modes using the asymptotic iteration method (AIM). We also study non-Hermitian PT symmetric potentials using AIM. The spectra, in all cases, are found to be in excellent agreement with exact results.     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.     

Coherence properties of a Bose-Einstein condensate in an optical superlattice

We study the effect of a one dimensional optical superlattice on the superfluid properties (superfluid fraction, number squeezing, dynamic structure factor) and the quasi-momentum distribution of the Mott-insulator. We show that due to the secondary lattice, there is a decrease in the superfluid fraction and the number fluctuation. The dynamic structure factor which can be measured by Bragg spectroscopy is also suppressed due to the addition of the secondary lattice. The visibility of the interference pattern (the quasi-momentum distribution) of the Mott-insulator is found to decrease due to the presence of the secondary lattice. Our results have important implications in atom interferometry and quantum computation in optical lattices.     

Atom waveguide and 1D optical lattice using a two-color evanescent light field around an optical micro/nano-fiber

We propose a two-color scheme of atom waveguides and one-dimensional （1D） optical lattices using evanescent wave fields of different transverse modes around an optical micro/nano-fiber. The atom guide potential can be produced when the optical fiber carries a red-detuned light with TE01 mode and a blue-detuned light with HEll mode, and the 1D optical lattice potential can be produced when the red-detuned light is transformed to the superposition of the TE01 mode and HE11 mode. The two trapping potentials can be transformed to each other for accurately controlling mode transformation for the red-detuned light. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.     

Theoretical study of the <Superscript>1,3</Superscript>Σ<Superscript>+</Superscript> states of the NaH molecule in the adiabatic and diabatic representations

Adiabatic and diabatic study for all the states dissociating below the ionic limit [i.e., Na (3s, 3p, 4s, 3d, 4p, 5s, 4d, and 4f) + H (1s)] in ¹Σ⁺ and ³Σ⁺ symmetries are presented. Adiabatic results are also reported for ^1,3Π and ^1,3Δ symmetries. Pseudo-potential, operatorial core-valence correlation, and full valence CI approaches combined with an efficient diabatization procedure are used in these ab initio calculations. Our vibrational-level spacings and spectroscopic constants are in good agreement with the available experimental data for the low-lying states. Diabatic potentials and dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The hydrogen electron affinity correction was taken into account by the use of the efficient diabatization method. This leads to a better agreement with the available experimental data. Experimental suggestions are also given for the higher excited states based on their unusual behavior.     

Semiclassical Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators

In this paper, we study an L ² version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant goes to zero.     

A note on Besov regularity of layer potentials and solutions of elliptic PDE's

Let be a second order, (variable coefficient) elliptic differential operator and let , , 0$">, satisfy in the Lipschitz domain . We show that can exhibit more regularity on Besov scales for which smoothness is measured in with . Similar results are valid for functions representable in terms of layer potentials.

     

A Radial Derivative with Boundary Values of the Spherical Poisson Integral

A formula of a radial derivative is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates .