Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose-Einstein condensate with a magnetic trap and an optical lattice （OL） trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional pe-riodic optical lattice potentials.The stationary state perturbation solutions of the coupled two-component nonlinearSchr?dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method.Theoretical analysisrevels that the perturbation solution is the chaotic one,which indicates the existence of chaos and chaotic region inparameter space.The corresponding numerical calculation results agree well with the analytical results.By applying thechaotic perturbation solution,we demonstrate the atomic spatial population and the energy distribution of the systemare chaotic generally.

Lattice potential energy and standard molar enthalpy in the formation of 1-dodecylamine hydrobromide (1-C_(12)H_(25)NH_3 ·Br)(s)

This paper reports that 1-dodecylamine hydrobromide （1 C12H25NH3.Br）（s） has been synthesized using the liquid phase reaction method. The lattice potential energy of the compound 1-C12H25NH3.Br and the ionic vol- ume and radius of the 1-C12H25NH3＋ cation are obtained from the crystallographic data and other auxiliary ther- modynamic data. The constant-volume energy of combustion of 1 C12H25NH3.Br（s） is measured to be AcUo（1 C12H25NH3.Br, s） = （7369.03-4-3.28） kJ.mo1-1 by means of an RBC-II precision rotating-bomb combustion calorime- ter at T=（298.15~0.001） K. The standard molar enthalpy of combustion of the compound is derived to be △cHo（1- C12H25NH3.Br, s）=- （7384.52±3.28） kJ.mo1-1 from the constant-volume energy of combustion. The standard molar enthalpy of formation of the compound is calculated to be △fHo（1-C12H25NH3.Br, s）=-（1317.86~3.67） kJ.mo1-1 from the standard molar enthalpy of combustion of the title compound and other auxiliary thermodynamic quantities through a thermochemical cycle.

Analytical Periodic Wave and Soliton Solutions of the Generalized Nonautonomous Nonlinear Schrdinger Equation in Harmonic and Optical Lattice Potentials

We construct analytical periodic wave and soliton solutions to the generalized nonautonomous nonlinear Schr6dinger equation with timeand space-dependent distributed coefficients in harmonic and optical lattice potentials. We utilize the similarity transformation technique to obtain these solutions. Constraints for the dispersion coefficient, the nonlinearity, and the gain （loss） coefficient are presented at the same time. Various shapes of periodic wave and soliton solutions are studied analytically and physically. Stability analysis of the solutions is discussed numerically.

Spectrum transformation and conservation laws of lattice potential KdV equation

Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In this paper, we derive infinitely many conserved quantities for the lattice potential Korteweg-de Vries equation whose solutions have nonzero backgrounds. The derivation is based on the fact that the scattering data a（z） is independent of discrete space and time and the analytic property of Jost solutions of the discrete Schr5dinger spectral problem. The obtained conserved densities are asymptotic to zero when ｜n｜ （or ｜m｜） tends to infinity. To obtain these results, we reconstruct a discrete Riccati equation by using a conformal map which transforms the upper complex plane to the inside of unit circle. Series solution to the Riccati equation is constructed based on the analytic and asymptotic properties of Jost solutions.

The Coherence of a Dipolar Condensate in a Harmonic Potential Superimposed to a Deep Lattice

Within the mean-field model, the coherent matter waves of a dipolar condensate in a harmonic potentiM super- imposed to a deep lattice are investigated by the variational princip]e. It is shown that, in a harmonic potential superimposed to a deep lattice, it is possible to control the decoherence of Bloch oscillations due to the fact that the on-site and the inter-site dipolar interactions can not only damp out Bloch oscillations but also maintain long-lived Bloch oscillations under the certain condition. In particular, long-lived Bloch oscillations of dipolar condensate can be realized when the dipolar interaction, the contact interaction, the frequency of the harmonic potentiM and initial width of the wave packet satisfy an analytical condition. Thus the decoherence of Bloch os- cillation can be controlled by adjusting the dipolar interaction, the contact interaction, the frequency of harmonic potentiM and the initial width of the wave packet.

Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schroinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain（loss）.Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed.