*[This is akin to a living review, which will hopefully improve from time to time. Last edited 2017-10-11.]*

This post will collect some models of decoherence and branching. We don’t have a rigorous definition of branches yet but I crudely define models of branching to be models of decoherence^{ a } which additionally feature some combination of amplification, irreversibility, redundant records, and/or outcomes with an intuitive macroscopic interpretation. I have the following desiderata for models, which tend to be in tension:

- computational tractability
- physically realistic
- symmetric (e.g., translationally)
- no ad-hoc system-environment distinction
- Ehrenfest evolution along classical phase-space trajectories (at least on Lyapunov timescales)

Regarding that last one: we would like to recover “classical behavior” in the sense of classical Hamiltonian flow, which (presumably) means continuous degrees of freedom.^{ b } Branching only becomes unambiguous in some large-*N* limit, so it seems satisfying models are necessarily messy and difficult to numerically simulate. At the minimum, a good model needs time asymmetry (in the initial state, not the dynamics), sensitive dependence on initial conditions, and a large bath. Most branching will (presumably) be continuous both in time and in number of branches, like a decaying atom where neither the direction nor time of decay are discrete.… [continue reading]