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Full-Text Articles in Social and Behavioral Sciences
A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers
European Mathematical Society 2018 We prove that, given any finite link L in R 3 , there is a high-energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.
Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers
For any finite link L in R3 we prove the existence of a complex-valued eigenfunction of the Coulomb Hamiltonian such that its nodal set contains a union of connected components diffeomorphic to L. This problem goes back to Berry, who constructed such eigenfunctions in the case where L is the trefoil knot or the Hopf link and asked the question about the general result.
Motion By Mixed Volume Preserving Curvature Functions Near Spheres, David James Hartley
Motion By Mixed Volume Preserving Curvature Functions Near Spheres, David James Hartley
Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers
In this paper we investigate the flow of hypersurfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact hypersurfaces without boundary that can be written as a graph over a sphere. The linearisation of the resulting fully nonlinear PDE is used to prove a short-time existence theorem for hypersurfaces that are sufficiently close to a sphere and, using centre manifold analysis, the stability of the sphere as a stationary solution to the flow is determined. We will find that for initial hypersurfaces sufficiently close to a sphere, the flow will exist …