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Topological quenching of the tunnel splitting for a particle in a double-well potential on a planar loop

Weigert, S. (orcid.org/0000-0002-6647-3252) (1994) Topological quenching of the tunnel splitting for a particle in a double-well potential on a planar loop. Physical Review A. pp. 4572-4581. ISSN 1094-1622

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The motion of a particle along a one-dimensional closed curve in a plane is considered. The only restriction on the shape of the loop is that it must be invariant under a twofold rotation about an axis perpendicular to the plane of motion. Along the curve a symmetric double-well potential is present leading to a twofold degeneracy of the classical ground state. In quantum mechanics, this degeneracy is lifted: the energies of the ground state and the first excited state are separated from each other by a slight difference ¿E, the tunnel splitting. Although a magnetic field perpendicular to the plane of the loop does not influence the classical motion of the charged particle, the quantum-mechanical separation of levels turns out to be a function of its strength B. The dependence of ¿E on the field B is oscillatory: for specific discrete values Bn the splitting drops to zero, indicating a twofold degeneracy of the ground state. This result is obtained within the path-integral formulation of quantum mechanics; in particular, the semiclassical instanton method is used. The origin of the quenched splitting is intuitively obvious: it is due to the fact that the configuration space of the system is not simply connected, thus allowing for destructive interference of quantum-mechanical amplitudes. From an abstract point of view this phenomenon can be traced back to the existence of a topological term in the Lagrangian and a nonsimply connected configuration space. In principle, it should be possible to observe the splitting in appropriately fabricated mesoscopic rings consisting of normally conducting metal.

Item Type: Article
Copyright, Publisher and Additional Information: © 1994 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 25 Mar 2016 14:21
Published Version: http://dx.doi.org/10.1103/PhysRevA.50.4572
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1363

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