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Quantum monodromy in the two-centre problem

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H Waalkens1,4, A Junge2,4 and H R Dullin3,4

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LETTER TO THE EDITOR

Using modern tools from the geometric theory of Hamiltonian systems it is shown that electronic excitations in diatoms which can be modelled by the two-centre problem exhibit a complicated case of classical and quantum monodromy. This means that there is an obstruction to the existence of global quantum numbers in these classically integrable systems. The symmetric case of H+2 and the asymmetric case of H He++ are explicitly worked out. The asymmetric case has a non-local singularity causing monodromy. It coexists with a second singularity which is also present in the symmetric case. An interpretation of monodromy is given in terms of the caustics of invariant tori.


PACS

03.65.Vf Phases: geometric; dynamic or topological

31.15.-p Calculations and mathematical techniques in atomic and molecular physics

02.30.Ik Integrable systems

03.65.Ge Solutions of wave equations: bound states

MSC

81V45 Atomic physics

58K10 Monodromy

81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (See also 14D05, 32S40)

Subjects

Atomic and molecular physics

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Dates

Issue 20 (23 May 2003)

Received 20 February 2003

Published 7 May 2003



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