Gyroscopic classical and quantum oscillators interacting with heat baths

We analyze the stability of a gyroscopic oscillator interacting with a finite- and infinite-dimensional heat bath in both the classical and quantum cases. We consider a finite gyroscopic oscillator model of a particle in a magnetic field and examine the stability before and after coupling to a heat bath. It is shown that if the oscillator is gyroscopically stable, coupling to a sufficiently massive heat bath induces instability. The meaning of these ideas in the quantum context is discussed. The model extends the exact diagonalization analysis of an oscillator and field of Ford, Lewis, and O´Connell to the gyroscopic setting