On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field

Details On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field

2001-07-11

arxiv.org/abs/quant-ph/0107063v1

Phys. Lett. A 287 (2001) 187-189

Physics

Quantum Physics

Accepted for publication in Phys. Lett. A

Scientific paper

10.1016/S0375-9601(01)00476-5

We consider a class of general spin Hamiltonians of the form $H_s(t)=H_0(t)+H'(t)$ where $H_0(t)$ 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 $H_s(t)$ admits the same dynamical invariant as $H_0(t)$. 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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