Spin evolution of spin-1 Bose-Einstein condensates

An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$ without using approximation. Therefore it goes beyond the mean field theory and provides a general, accurate, and complete description for the whole process of non-dissipative evolution starting from various initial states. The numerical results directly given by the formula coincide qualitatively well with existing experimental data, and also with other theoretical results from solving dynamic differential equations. For some special cases of initial state, instead of undergoing strong oscillation as found previously, the evolution is found to go on very steadily in a very long duration.Comment: 7 pages, 3 figures

Convergence rate of dimension reduction in Bose-Einstein condensates

In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence rates for the dimension reduction of 3D ground state and dynamics of the GPE in the case of disk-shaped condensation and cigar-shaped condensation are reported based on our asymptotic and numerical results. In addition, the parameter regimes in which the 3D GPE cannot be reduced to lower dimensions are identified.Comment: 27pages; 9 figure

Deduction of the quantum numbers of low-lying states of 6-nucleon systems based on symmetry

The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be mainly {4,2} and {2,2,2}.Comment: 8 pages, no figure

A time-splitting spectral scheme for the Maxwell-Dirac system

We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition, is unconditionally stable and highly efficient as our numerical examples show. In particular we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter \dt, which is the ratio of the characteristic speed and the speed of light.Comment: 29 pages, 119 figure

Tree-level Split Helicity Amplitudes in Ambitwistor Space

We study all tree-level split helicity gluon amplitudes by using the recently proposed BCFW recursion relation and Hodges diagrams in ambitwistor space. We pick out the contributing diagrams and find that all of them can be divided into triangles in a suitable way. We give the explicit expressions for all of these amplitudes. As an example, we reproduce the six gluon split NMHV amplitudes in momentum space.Comment: 20 pages, 16 figures; minor changes; clarifications added, 22 pages, 16 figure

Multi-breathers and high order rogue waves for the nonlinear Schr\"odinger equation on the elliptic function background

We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The dynamics of the breathers in the presence of various kinds of backgrounds such as dn, cn, and non-trivial phase-modulating elliptic solutions are presented, and their behaviors dependent on the effect of backgrounds are elucidated. We also determine the asymptotic behaviors for the multi-breather solutions with different velocities in the limit $t\to\pm\infty$, where the solution in the neighborhood of each breather tends to the simple one-breather solution. Furthermore, we exactly solve the linearized NLSE using the squared eigenfunction and determine the unstable spectra for elliptic function background. By using them, the Akhmediev breathers arising from these modulational instabilities are plotted and their dynamics are revealed. Finally, we provide the rogue-wave and higher-order rogue-wave solutions by taking the special limit of the breather solutions at branch points and the generalized Darboux transformation. The resulting dynamics of the rogue waves involves rich phenomena: depending on the choice of the background and possessing different velocities relative to the background. We also provide an example of the multi- and higher-order rogue wave solution.Comment: 45 pages, 16 figure

Discovery of a nearby young brown dwarf binary candidate

In near-infrared NaCo observations of the young brown dwarf 2MASS J0041353-562112, we discovered a companion a little less than a magnitude fainter than the primary. The binary candidate has a separation of 143 mas, the spectral types are M6.5 and M9.0 for the two components. Colors and flux ratios are consistent with the components being located at the same distance minimizing the probability of the secondary being a background object. The brown dwarf is known to show Li absorption constraining the age to less than ~200 Myr, and it was suspected to show ongoing accretion, indicating an age as low as ~10 Myr. We estimate distance and orbital parameters of the binary as a function of age. For an age of 10 Myr, the distance to the system is 50 pc, the orbital period is 126 yr, and the masses of the components are ~30 and ~15 MJup. The binary brown dwarf fills a so far unoccupied region in the parameters mass and age; it is a valuable new benchmark object for brown dwarf atmospheric and evolutionary models.Comment: 4 pages, 2 figures, accepted by A&

Two-body scattering in a trap and a special periodic phenomenon sensitive to the interaction

Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be accumulated. Two periodic phenomena with a shorter and a much longer period, respectively, are found. The latter is sensitive to the interaction. Instead of measuring the differential cross section as usually does, the measurement of the longer period and the details of the periodic behavior might be a valid source of information on weak interactions among neutral particles.Comment: 5 pages, 5 figure