Chaotic Rotation from NonLinear Quantum Mechanics. I

Shigemi ARAKI

Shigemi Araki

Satoshi Adachi

Abstruct.The semiclassical coherent state path integral developed by Klauder is evaluated numerically for a chaotic system (the kicked rotator).This evaluation needs the complexfied classical dynamics of the system and involves a proper treatment of the Stokes phenomenon caused by a new caustic, named \ l a n g l e \ l a n g l e Phase Space Caustic (PSC) ) \ r a n g l e .It is revealed that the chaotic natute of the dynamics produces PSC's.This investigation suggests that complex classical mechanics has a clear physical reality.

Giulio Casati

Emilio Fiordilino

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.

Robert C. Bishop