Potential Scattering on a Spherical Surface
| Autor: | Tin-Lun Ho, Jian Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Physics
Surface (mathematics) Length scale Angular momentum Scattering Plane (geometry) FOS: Physical sciences Condensed Matter Physics Curvature 01 natural sciences Atomic and Molecular Physics and Optics 010305 fluids & plasmas Quantum Gases (cond-mat.quant-gas) 0103 physical sciences Bound state Atomic physics 010306 general physics Condensed Matter - Quantum Gases Energy (signal processing) |
| Popis: | The advances in cold atom experiments have allowed construction of confining traps in the form of curved surfaces. This opens up the possibility of studying quantum gases in curved manifolds. On closed surfaces, many fundamental processes are affected by the local and global properties, i.e. the curvature and the topology of the surface. In this paper, we study the problem of potential scattering on a spherical surface and discuss its difference with that on a 2D plane. For bound states with angular momentum $m$, their energies ($E_{m}$) on a sphere are related to those on a 2D plane ($-|E_{m,o}|$) as $E_{m}= - |E_{m, o}| + E_{R}^{} \left[ \frac{m^2-1}{3} + O\left( \frac{r_o^2}{R^2} \right) \right] $, where $E_{R}^{} = \hbar^2/(2M R^2)$, and $R$ is the radius of the sphere. Due to the finite extent of the manifold, the phase shifts on a sphere at energies $E\sim E_{R}^{}$ differ significantly from those on a 2D plane. As energy $E$ approaches zero, the phase shift in the planar case approaches $0$, whereas in the spherical case it reaches a constant that connects the microscopic length scale to the largest length scale $R$. 5 pages, 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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