Branched Hamiltonians and Supersymmetry

Understand

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek.

• These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles.
• A basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.