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- W2084298052 abstract "The phase of a quantum state changes rapidly as parameters X = ( X 1 , X 2 ,...) are varied near a degeneracy X *, reflecting the monopole singularity of the underlying phase 2-form V ( X ) at X *. The singularities may be sources or sinks of V . We study them numerically and display them graphically for two families of hamiltonians whose degeneracy structure is typical. First is a particle moving along a line segment with kinetic energy quartic in the momentum (‘quartic-momentum square well’); the X are incorporated into the boundary conditions. Second is a charged particle moving in a domain D of the plane which is threaded by a magnetic flux line of strength α, with wavefunction vanishing on the boundary ∂D (‘Aharonov-Bohm billiards’); the X are α and parameters specifying ∂D; V is not invariant under gauge transformations of the vector potential generating the flux. For Aharonov-Bohm billiards we study how the spatial patterns of phase of wavefunctions change round circuits near degeneracies; these patterns also have singularities (wavefront dislocations) that appear and disappear by colliding with each other and with ∂D." @default.
- W2084298052 created "2016-06-24" @default.
- W2084298052 date "1989-08-08" @default.
- W2084298052 modified "2023-09-25" @default.
- W2084298052 title "The quantum phase 2-form near degeneracies: two numerical studies" @default.
- W2084298052 cites W2044154336 @default.
- W2084298052 doi "https://doi.org/10.1098/rspa.1989.0081" @default.
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