Three-body recombination in bose gases with large scattering length

An effective field theory for the three-body system with large scattering length is applied to three-body recombination to a weakly bound s-wave state in a Bose gas. Our model independent analysis demonstrates that the three-body recombination constant alpha is not universal, but can take any value between zero and 67.9Planck's over 2pia(4)/m, where a is the scattering length. Other low-energy three-body observables can be predicted in terms of a and alpha. Near a Feshbach resonance, alpha should oscillate between those limits as the magnetic field B approaches the point where a-->infinity. In any interval of B over which a increases by a factor of 22.7, alpha should have a zero.     

On the exact treatment of time-dependent self-interaction correction

We present a new formulation of the time-dependent self-interaction correction (TDSIC). It is derived variationally obeying explicitly the constraints on orthonormality of the occupied single-particle orbitals. The thus emerging rather involved symmetry condition amongst the orbitals is dealt with using two separate sets of (occupied) single-particle wavefunctions, related by a unitary transformation. The double-set TDSIC scheme is well suited for numerical implementation. We present results for laser-excited dynamics in a 1D model for a molecule and in fully fledged 3D calculations.     

An exact treatment of some integrals appearing in the three-body contributions to transport coefficients

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the switching parameter ε.     

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose--Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature ({\em Phys. Rev. Lett.} {\bf 94} (2005) 050402 and {\em Chin. Phys. Lett.} {\bf 22} (2005) 1855).     

Relativistic three-body recombination with the QED vacuum

Electron-positron pair annihilation into a single photon is studied when a second free electron is present. Focussing on the relativistic regime, we show that the photon emitted in the three-lepton interaction may exhibit distinct angular distributions and polarization properties. Moreover, the process can dominate over two-photon annihilation in relativistic electron-positron plasmas of few-MeV temperature. An analogy with three-body recombination of electrons with ions is drawn.     

Nonautonomous bright and dark solitons of Bose-Einstein condensates with Feshbach-managed time-dependent scattering length

We present a family of nonautonomous bright and dark soliton solutions of Bose-Einstein condensates with the time-dependent scattering length in an expulsive parabolic potential. These solutions show that the amplitude, width, and velocity of soliton can be manipulated by adjusting the atomic scattering length via Feshbach resonance. For the cases of both attractive and repulsive interactions, the total particle number is a conservation quantity, but the peak (dip) density can be controlled by the Feshbach resonance parameter. Especially, we investigate the modulation instability process in uniform Bose-Einstein condensates with attractive interaction and nonvanishing background, and clarify that the procedure of pattern formation is in fact the superposition of the perturbed dark and bright solitary waves. At last, we give the analytical expressions of nonautonomous dark one- and two-soliton solutions for repulsive interaction, and investigate their properties analytically.     

Multiple scattering with three-body forces

The multiple-scattering formalism is generalized to account for simultaneous interactions of a projectile with two target particles. In the cluster expansion of multiple-scattering theory such three-body interactions combine with iterates of two-body interactions. Some comparisons of multiple scattering with the Faddeev theory are given.     

Dynamics of matter-wave solitons in Bose-Einstein condensates with time-dependent scattering length and complex potentials

We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D)Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) withtime-dependent scattering length in varying trapping potentials with feeding/loss term. Byperforming a modified lens-type transformation, we reduce the GP equation into a classicalnonlinear Schrödinger (NLS) equation with distributed coefficients and find its integrablecondition. Under the integrable condition, we apply the generalized Jacobian ellipticfunction method (GJEFM) and present exact analytical solutions which describe thepropagation of a bright and dark solitons in BECs. Their stability is examined usinganalytic method. The obtained exact solutions show that the amplitude of bright and darksolitons depends on the scattering length, while their motion and the total number of BECatoms depend on the external trapping potential. Our results also shown that the loss ofatoms can dominate the aggregation of atoms by the attractive interaction, and thus thepeak density can decrease in time despite that the strength of the attractive interactionis increased.     

An exact multiple scattering calculation in comparison with the Fresnel approximation

An exact solution to the problem of nucleon scattering from two fixed potentials is compared with its Fresnel approximation. The differential cross sections are found to be in good agreement over the entire range of scattering angles.     

More exact invariants for the time-dependent harmonic oscillator

We derive an infinite number of new invariants and related auxiliary equations for the time-dependent harmonic oscillator.     

A non-singular equation for the three-body scattering problem

This paper derives a non-singular integral equation for the three-body problem. Starting from the three-body equations obtained by Karlsson and Zeiger we introduce a set of algebraic transformations that remove all the Green function pole singularities. For scattering energies on the real axis we find a singularity-free momentum-space integral equation. This equation requires only a finite range of momentum values for its solution. In the case of well-behaved two-body interactions, such as the superposition of Yukawa interactions, we prove that the kernels of this equation have a finite Hilbert-Schmidt norm. This same norm provides a general criteria for establishing when the impulse approximation is accurate.     

Anomalous diffusion with absorption: exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.     

On the three-body Coulomb scattering problem

We describe the smoothness properties and the asymptotic form of the Green's function (in configuration space) for three charged particles. We also discuss the integral equations and the boundary value problems for the Coulomb wavefunctions and we show that they form a complete set. Finally, we study the singularities of the Coulomb scattering operator, and we investigate the connection between the Dollard wave operators and the Coulomb wavefunctions.     

On the three-body long-range scattering problems

In this Letter, we give results on precise microlocalized time-decay estimates in three-body long-range scattering problems. We prove the asymptotic completeness of wave operators in three-body long-range scattering for a class of long-range interactions of the form V ₁(x)+V ₂(x), where V ₁ is nonnegative and decays like O(|x|^–0), for some ₀ > 1/2 and V ₂ decays like O(|x|^-y) for some > 2(1–₀)/₀.     

An exact iterative solution of the atom-surface scattering problem for realistic potentials

A general method, based on high order distorted wave perturbation theory, is developed to obtain exact reflection intensities for low energy atoms scattered by solid surfaces. Resonance shapes are calculated using projection techniques to obtain uniform convergence. Important differences with the hard corrugated wall model arise when the calculations for a corrugated Morse potential are compared with experiment for helium scattered by a Cu(110) surface.     

Solutions of the exact time-dependent microbending equations

Bandwidth improvement factor and losses of two-dimensional fibers with power-law index profiles, submitted to microbends with power-law curvature spectra, are given here in a graphical form. The domain of validity of the analytical solutions is discussed.     

A novel method for solving the three-body scattering problem

A numerical scheme for solving a three-body scattering problem within the framework of the configuration space Faddeev equations in three-dimension, i.e., without resort to explicit partial wave expansion, is presented. The method is applied to calculate the low-energy n-d observables.     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

On the Fokker-Planck theory of electron three-body recombination

The Fokker-Planck theory of electron three-body recombination based on the concept of electron diffusion along the energy scale in the excited hydrogen-like atoms formed in the recombining plasmas, is extended in several respects. 1. An universal formula for population distribution of the excited atoms in strongly ionized plasmas was found under a sole assumption, that the cross-sections for the inelastic atom-electron collisions are governed by the classical impulse approximation. 2. A general Fokker-Planck theory of the recombination in a slightly ionized, two-temperature plasmas was formulated. The recombination coefficients for such plasmas were shown to possess some peculiar properties in case the electronic temperature differs appreciable from the atomic one. A few limitations of the existing schemas for calculation of the recombination kinetics are briefly discussed.     

Chaotic scattering in the gravitational three-body problem

We summarize some results of an ongoing study of the chaotic scattering interaction between a bound pair of stars (a binary) and an incoming field star. The stars are modeled as point masses and their equations of motion are numerically integrated for a large number of initial conditions. The global features of the resulting initial-value space maps are presented, and their evolution as a function of system parameters is discussed. We find that the maps contain regular regions separated by rivers of chaotic behavior. The probability of escape within the chaotic regions is discussed, and a straightforward explanation of the scaling present in these regions is reviewed. We investigate a statistical quantity of interest, namely the cross section for temporarily bound interactions, as a function of the third star's incoming velocity and mass. Finally, a new way of considering long-lived trajectories is presented, allowing long data sets to be qualitatively analyzed at a glance.