Wave packets from the spectrum

Abstract

The freedom to change Fock basis seems to ensure a minimum amount of locality in lattice theories in the following sense: If $\{({\hat{a}}_i^{†},{\hat{a}}_i)\}$ for $i=1,\dots ,n$ is a lattice of creation and annihilation operators and if a given Hamiltonian $\hat{H}$ induces highly non-local dynamics on that lattice, then it will usually be possible to change to a new set of operators $\{({\hat{b}}_i^{†},{\hat{b}}_i)\}$ in terms of which the dynamics appear less non-local. We demonstrate this by turning a highly non-local random matrix model into a local, 1D lattice theory where particles can propagate in localized wave packets. More generally, we show that any Hamiltonian can be made to look like such a theory, with the lattice dispersion relation and the non-integrability of the theory depending on the spectrum of $\hat{H}$. We argue that our results are a step towards quantum mereology for fields.

20 pages + appendix; public code available