arXiv subjects

Nicolai Nygaard

Publications and source records attributed to Nicolai Nygaard.

4 recordsLinked to original sources

arXiv2012

Scattering of matter wave solitons on localized potentials

We present numerical and analytical results for the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. Our mean field analysis identifies regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate of atoms with repulsive interactions, we find different reflection and transmission properties of the dark and the bright components.

cond-mat.quant-gas↗

arXiv2006

A two-channel R-matrix analysis of magnetic field induced Feshbach resonances

A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled channels calculations. Using R-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.

cond-mat.other↗

arXiv2004

Comments on the Discrete Variable Representation

We discuss the application of the Discrete Variable Representation to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well-behaved, the boundary conditions are satisfied and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

physics.chem-ph↗

arXiv1999

Component separation in harmonically trapped boson-fermion mixtures

We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anisotropic harmonic traps. We investigate the phenomenon of component separation as function of the strength of the inter-particle interaction. While solving a Gross-Pitaevskii mean field equation for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum mechanical Slater determinant Schrödinger equation.

cond-mat↗