Has anyone come across any physical applications of a linear theory where Hamiltonians are proportional to an arbitrary order of momentum? This paper


details the free particle eigenvalue for a Hamiltonian that depends quartically on the momentum, but I couldn't find much more.

  • $\begingroup$ Linear theory ?? The whole Hamiltonian proportional to a power of momentum? What would you have in mind? Typically Kerr oscillators, nonlinear optics, etc. run on piers of creation and annihilation operators, and so do studies of chaos. But fro the plain vanilla theories of your type, only magnetism. $\endgroup$ – Cosmas Zachos Jan 6 at 1:26

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