New energetic and dynamic quantum effects originating from the breaking of time-reversal symmetry

The reduction of spatial symmetry can have qualitative effects for a given quantum system, such as splitting of energy levels that are degenerate in the unperturbed case. Can the breaking of temporal symmetry have a similar effect? Using a nonlinear quantum mechanical model to describe the effective interaction of simple, exactly solvable quantum systems with some dissipative environment, the time-symmetry-breaking effect of this interaction on the ground-state energy of these systems can be studied analytically. Also, in the case of dynamical properties such as tunnelling currents, the breaking of time-reversal symmetry can have quite unexpected effects. In general, a dissipative environment is assumed to inhibit the motion of a dynamical system, e.g., by reducing the frequency and amplitude of a harmonic oscillator. Our study shows, however, that under certain resonance-like conditions, the interaction with the environment can also create currents that are not present in the unperturbed system. These results follow directly from the analytical solutions of our model.