Nonlinear Quantum Dynamics

Abstract

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.

13 pages, 3 figures, invited talk at the NATO Advanced Workshop, "Nonlinear Dynamics and Fundamental Interactions," (October, 2004, Tashkent)

References in corpus (6)

• Quantum Continual Measurements and a Posteriori Collapse on CCR
• Feedback cooling of a nanomechanical resonator
• Bayesian feedback versus Markovian feedback in a two-level atom
• Quantum Feedback Control of Atomic Motion in an Optical Cavity
• Measurement induced quantum-classical transition
• Quantum feedback control of a solid-state qubit

Cited by in corpus (2)

• Classical to quantum transition of a driven nonlinear nanomechanical resonator
• Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics