Dissipation and quantization

We show that the dissipation term in the Hamiltonian for a couple of classical damped-amplified oscillators manifests itself as a geometric phase and is actually responsible for the appearance of the zero point energy in the quantum spectrum of the 1D linear harmonic oscillator. We also discuss the thermodynamical features of the system. Our work has been inspired by 't Hooft proposal according to which information loss in certain classical systems may lead to ``an apparent quantization of the orbits which resembles the quantum structure seen in the real world".