Random phase wave: A soluble non-Markovian system

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Abstract
The averaged propagator and the corresponding mass operator (non‐Markovian particle‐wave collision operator) of a particle being accelerated by a random potential are constructed explicitly in a model system. The model consists of an ensemble of monochromatic waves of random phase, such as arises in narrow‐bandwidth plasma turbulence, and is particularly interesting as a system exhibiting strong trapping. An essential simplifying feature is that the propagator is evaluated in oscillation‐center picture, which greatly simplifies the momentum‐space operators occurring in the problem, and leads to a remarkable factorization of the mass operator. General analyticity and symmetry properties are derived using a projection‐operator method, and verified for the solution of the model system. The nature of the memory exhibited by the mass operator is briefly examined.