ua nt - p h / 06 02 11 5 v 1 1 4 Fe b 20 06 Is there a prescribed parameter ’ s space for the adiabatic geometric phase ? ∗
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چکیده
The Aharonov–Anandan and Berry phases are determined for the cyclic motions of a non–relativistic charged spinless particle evolving in the superposition of the fields produced by a Penning trap and a rotating magnetic field. Discussion about the selection of the parameter’s space and the relationship between the Berry phase and the symmetry of the binding potential is given. PACS: 03.65 Ca, 03.65 Sq. Published in Europhysics Letters 21 (1993) 148-152 On leave of absence, Departamento de F́ısica, Cinvestav-IPN, A.P. 14-740, 07000México D.F., Mexico In 1984 Berry [1] discovered a geometric phase, which now is known as Berry’s or adiabatic phase and usually arises when an eigenstate of the Hamiltonian H(X(t)) evolves cyclically and adiabatically due to a cyclic and slow change of the parameters X(t). That phase was identified as a geometric property of the space of all possible values of X(t) (the parameter space) [2] and gave rise to the present interest on the geometric aspects of quantum theory [3–7]. An important generalization which does not need the adiabatic assumption (or equivalently that the initial state be an eigenstate of H(X(t))) was proposed by Aharonov and Anandan [3]. The essential requirement in the Aharanov– Anandan (AA) treatment is that the system performs a cyclic motion |ψ(T )〉 = e|ψ(0)〉, then the geometric phase is given by:
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تاریخ انتشار 1992