We propose that a quantum operator, apart from representing quantum dynamics, may also represent a dynamical (steady-state) situation of a classical system. We consider a Hamiltonian that describes hopping of single (spinless, noninteracting) bosons to nearest-neighbor sites in a hypercubic lattice and find exactly the mass distribution (in arbitrary dimension) for the ground state and the first excited state. The density shows a peak at a mass equal to the density. A variant of this Hamiltonian is shown to have an exponential mass distribution (in the ground state) that is identical with an analogous classical model.

• Received 16 November 1999

DOI:https://doi.org/10.1103/PhysRevE.62.2945