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A note on the Berry phase for systems having one degree of freedom

1988; Institute of Physics; Volume: 21; Issue: 7 Linguagem: Inglês

10.1088/0305-4470/21/7/033

1361-6447

R. Simon, Naveen Kumar,

Synthesis and Properties of Aromatic Compounds

A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.