  The possibility of using nanoelectromechanical systems as a simulation tool
for quantum many-body effects is explored. It is demonstrated that an array of
electrostatically coupled nanoresonators can effectively simulate the
Bose-Hubbard model without interactions, corresponding in the single-phonon
regime to the Anderson tight-binding model. Employing a density matrix
formalism for the system coupled to a bosonic thermal bath, we study the
interplay between disorder and thermalization, focusing on the delocalization
process. It is found that the phonon population remains localized for a long
time at low enough temperatures; with increasing temperatures the localization
is rapidly lost due to thermal pumping of excitations into the array, producing
in the equilibrium a fully thermalized system. Finally, we consider a possible
experimental design to measure the phonon population in the array by means of a
superconducting transmon qubit coupled to individual nanoresonators. We also
consider the possibility of using the proposed quantum simulator for realizing
continuous-time quantum walks.
