Berrys geometrical phases in ESR in the presence of a stochastic process

Berrys [Proc. R. Soc. London, Ser. A 392, 45 (1984)] geometrical phase is discussed in the context of dissipative evolution of an interacting spin system, governed by the stochastic Liouville equation. An analytical treatment is given for a possible ESR experiment on an interacting electron-nucleus system, modulated by two-site jumps. Geometrical phases are shown to be relevant to systems of this type, when their Hamiltonian changes slowly with time. A method for obtaining higher-order corrections to the adiabatic approximation is demonstrated. It is found that if the jumps are slow relative to the rate of change of the Hamiltonian, their effect reduces to familiar line broadening, and the geometrical phases may be observed experimentally. Equations are also set up for a similar ESR experiment on an electron-nucleus system undergoing isotropic rotational diffusion, and a brief discussion of the equations follows.