On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field
Ali Mostafazadeh
Abstract
We consider a class of general spin Hamiltonians of the form Hs(t)=H0(t)+H'(t) where H0(t) and H'(t) describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the spins, respectively. We show that if H'(t) is rotationally invariant, then Hs(t) admits the same dynamical invariant as H0(t). A direct application of this observation is a straightforward rederivation of the results of Yan et al [Phys. Lett. A, Vol: 251 (1999) 289 and Vol: 259 (1999) 207] on the Heisenberg spin system in a changing magnetic field.
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