Projection Operator Approaches to Complex Susceptibility(Frontiers in Nonequilibrium Physics-Fundamental Theory, Glassy & Granular Materials, and Computational Physics-)

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We review two kinds of approaches to obtain the complex susceptibility with using the projection operator methods in Schrodinger and Heisenberg picture. In the complex susceptibility, we include the effect of initial correlation between the relevant system and its environment. Using the method in Heisenberg picture, we show a way to obtain the time evolution of a dynamical variable up to higher orders of system-environment interaction. We apply it to a case of low field resonance where a 1/2 spin interacts with a quantum environment. When we assume the spectral function for system-environment interaction to be described by a Lorentzian function, we find a continued fraction form of the memory term, which enables us to evaluate an arbitrary order of system-environment interaction up to infinite orders. We also show that the method in Schrodinger picture can be used to obtain the time evolution of the response function. With the method, we find a systematic way to treat a multiple-spin system under the effects of its environment. We demonstrate the usefulness of the method by applying it to a three-spin system which interacts with a quantum environment in the Ohmic spectral function.
2010-07-27