  Lattice softness has a significant impact on charge carrier dynamics in
condensed matter systems, contributing to the emergence of various properties
and functions. Examples include the remarkable carrier lifetimes and defect
tolerances of hybrid organic-inorganic perovskites. Recent studies suggest the
contribution of quartic anharmonicity of the lattice vibrations. The quartic
anharmonicity can be discussed with a double-well potential, and the transition
between the two minima can be coarse-grained as a two-state jump stochastic
process. Such a stochastic approach is typically employed to describe dynamic
fluctuations introduced into a system by two-state transitions in the
surroundings. To investigate charge transport in materials, however, it is
crucial to describe not only the fluctuations but also the dynamic lattice
distortion associated with charge transport. Therefore, there is a need for a
theory to describe the charge carrier dynamics proceeding alongside the lattice
distortion dynamics. In this study, we present a theory that describes quantum
dynamics under the influence of an environment with two stable states, termed a
bistable environment. The theory describes the effects of fluctuations and
dissipation induced from the bistable environment in a reasonable manner, and
the effects exhibit a different temperature dependence than the widely employed
Gaussian environment. The physical implication of this temperature dependence
is provided in terms of the environmental dynamics. The results of this study
are expected to provide a step forward in describing charge carrier dynamics in
materials with lattice softness and pronounced lattice anharmonicity, e.g.,
hybrid organic-inorganic perovskites. Moreover, these findings represent an
advancement in our understanding of and capacity to predict and control the
physical properties and functions of these materials.
