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Geometric quantization of mechanical systems with time-dependent parameters

G. Giachetta·L. Mangiarotti·G. Sardanashvily
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Abstract

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the adiabatic assumption. A Hamiltonian of such a system is affine in the temporal derivative of parameter functions. This leads to the geometric Berry factor phenomena.

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G. Giachetta, L. Mangiarotti, G. Sardanashvily. 2001-12-29. Geometric quantization of mechanical systems with time-dependent parameters. https://doi.org/10.1063/1.1477262

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