2 research outputs found
Adiabatic theorems for generators of contracting evolutions
We develop an adiabatic theory for generators of contracting evolution on
Banach spaces. This provides a uniform framework for a host of adiabatic
theorems ranging from unitary quantum evolutions through quantum evolutions of
open systems generated by Lindbladians all the way to classically driven
stochastic systems. In all these cases the adiabatic evolution approximates, to
lowest order, the natural notion of parallel transport in the manifold of
instantaneous stationary states. The dynamics in the manifold of instantaneous
stationary states and transversal to it have distinct characteristics: The
former is irreversible and the latter is transient in a sense that we explain.
Both the gapped and gapless cases are considered. Some applications are
discussed.Comment: 31 pages, 4 figures, replaced by the version accepted for publication
in CM