Application of B-splines to determining eigen-spectrum of Feshbach molecules

Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps

We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering amplitude for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single channel s-wave scattering of $^{23}$Na atoms in an iso…

镝费什巴赫谱中共存的规则与混沌动力学

Coexisting Regular and Chaotic Dynamics in the Dysprosium Feshbach Spectrum

通过精确校准$^{162}$Dy的费什巴赫谱并测量80多个共振的微分磁矩，发现磁矩分布中心附近的共振显示增强的能级排斥，而低边缘的共振接近泊松统计，揭示了混沌谱中的隐藏结构。

B-Spline basis Hartree-Fock method for arbitrary central potentials: atoms, clusters and electron gas

An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline basis in a finite-size box. Convergence of the self-consistency iterations for the occupied electron orbitals is achieved by increasing the magnitude of the electron-electron Coulomb interaction gradually to its true value. For the Coulomb central potential, convergence patterns and energies are presented for a selection of atoms and negative ions, and are …

Detecting level crossings without looking at the spectrum

In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of finding such crossings via a mapping to the problem of locating the roots of a polynomial in that parameter. We demonstrate our method on atoms and molecules in a magnetic field, where it has implications in the search for Feshbach resonances. In the atomic case our method allows us to point out a new class of invariants of the Breit-Rabi Hamiltonian of magnetic…