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A unified model for Diffusion Localization and Dissipation , optionally termed Diffusion with Local Dissipation, has been introduced for the study of Quantal Brownian Motion in dynamical disorder. It can be regarded as a generalization of the familiar Caldeira-Leggett model.
H = p 2 2 m + V + H i n t + H b a t h {\displaystyle {\mathcal {H}}={\frac {p^{2}}{2m}}+V+{\mathcal {H}}_{int}+{\mathcal {H}}_{bath}}
H b a t h = ∑ α {\displaystyle {\mathcal {H}}_{bath}=\sum _{\alpha }\left}
H i n t = − ∑ α c α Q α u {\displaystyle {\mathcal {H}}_{int}=-\sum _{\alpha }c_{\alpha }Q_{\alpha }u}