We construct and study a version of the Berry-Keating operator with a built-in
truncation of the phase space, which we choose to be a two-dimensional torus. The
operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic
oscillator, producing a difference operator on a finite, periodic lattice. We investigate
the continuum and the infinite-volume limit of our model in conjunction with the
semiclassical limit. Using semiclassical methods, we show that a specific combination
of the limits leads to a logarithmic mean spectral density as it was anticipated by
Berry and Keating
