Decoherent histories from local quench in integrable environment

We present a new approach to coarse-grained descriptions of an open quantum systems, enabling the explicit construction of multi-time decoherent histories in a controlled way. The method applies even in non-Markovian and integrable regimes and is based on treating the environment as a “tape recorder”. Environmental modes sequentially interact with the system and then irreversibly decouple, storing stable records of its past. This temporal coarse-graining provides the projections needed for consistent histories and allows an explicit evaluation of the decoherence functional. Numerical results for a local quench in an integrable environment show exponential suppression of off-diagonal terms relative to a significance threshold. Moreover, this provides a natural definition of history entropy, defined by the information irreversibly carried away by decoupled modes. It distinguishes dynamical regimes such as integrability versus chaos and offers a new diagnostic tool for out-of-equilibrium dynamics.