Generalized Geometrical Phase in the Case of Continuous Spectra

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.

7 pages, 2 figures

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Cited by in corpus (8)

• The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
• Fast adiabatic evolution by oscillating initial Hamiltonians
• Adiabatic theorems for linear and nonlinear Hamiltonians
• Geometric phases in a scattering process
• Quantum adiabatic evolution with energy-degeneracy levels
• Berry curvature, horocycles and scattering states in $Ad{S}_3/CF{T}_2$
• Mixed-Integer Programming Using a Bosonic Quantum Computer
• Hierarchical Theory of Quantum Adiabatic Evolution