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RESEARCH PRODUCT

Berry’s Phase

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Let a physical system be described by a Hamiltonian with two sets of variables \(\boldsymbol{r}\) and \(\boldsymbol{R}(t):\, H(\boldsymbol{r},\boldsymbol{R}(t)).\) The dynamical degrees of freedom \(\boldsymbol{r}\) (not necessarily space variables) are also called fast variables. The external time dependence is given by the slowly varying parameters \(\boldsymbol{R}(t) =\{ X(t),\,Y (t),\,\ldots,\,Z(t)\}\); consequently, the \(\boldsymbol{R}(t)\) are called slow variables.