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arXiv · 0804.4082

Generalized Geometrical Phase in the Case of Continuous Spectra

M. Maamache·Y. Saadi
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Abstract

A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An explicit formula for a generalized geometrical phase is derived in terms of the eigenstates of the Hamiltonian. As an illustration the generalized geometrical phase is calculated for relativistic spinning particles in slowly-changing electromagnetic fields. It is shown that the the S-matrix and the usual scattering (with negligible reflexion) phase shift can be interpreted as a generalized geometrical phase.

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M. Maamache, Y. Saadi. 2008-04-25. Generalized Geometrical Phase in the Case of Continuous Spectra. https://doi.org/10.1103/physrevlett.101.150407

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