Limit Cycles in Quantum Mechanics

Dipankar Home

Craig M. Savage

We investigate quantum-mechanical second-harmonic generation for parameters such that classical electrodynamics predicts oscillations. Specifically we calculate the Q distribution function in a Gaussian approximation about the classical limit cycle. In the classical limit initial rapid collapse of the Q distribution into the neighborhood of the limit cycle is followed by diffusion around the limit cycle. The experimental significance of this quantum diffusion is discussed.

Luis de la Peña, Ana Marı́a Cetto

Dipankar Home, S. Sengupta

Wagel Siegel

Eyal Buks

The problem of quantum measurement can be partially resolved by incorporating a process of spontaneous disentanglement into quantum dynamics. We propose a modified master equation, which contains a nonlinear term giving rise to both spontaneous disentanglement and thermalisation. We find that the added nonlinear term enables limit cycle steady states, which are prohibited in standard quantum mechanics. This finding suggests that an experimental observation of such a limit cycle steady state can provide an important evidence supporting the spontaneous disentanglement hypothesis.