Phase retrieval problem in quantum chaos

Mikito Toda

Asher Peres

Mikito Toda

New ideas are presented which relate dynamical features of quantum systems corresponding to chaos (so called “quantum chaos”) with the origin of irreversibility. They are based on studying topological defects of phase in the Husimi representation. Dynamical process leading to random phase is found in “quantum chaos”. The role of this for the origin of irreversibility is discussed from the following two points: (i) phase retrieval problem; (ii) entanglement of phase defects.

P. Lebœuf

Steven Tomsovic

Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of some of the most important Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum chaos research problems. The overall emphasis is on intuitive explanations and illustrations of various ideas with the references containing more mathematically rigorous expositions. The chapter begins with a description of various useful theoretical and computational tools of chaos research, e.g.~surfaces of section, paradigms of chaos, stability analysis, and symbolic dynamics... This is followed by discussions regarding the geometry of chaos, how chaotic systems respond to perturbations, and the complexification of Hamiltonian dynamics. Most of the contents concern topics that are long established and well known by now. The exceptions involve complications that arise from the complexification of phase space variables and time. There are relatively recent results summarized regarding the appropriate branches of determinant phases and how to distinguish complex trajectories that are associated with classically allowed processes versus those associated with non-allowed ones.

Mikito Toda

New ideas are presented which relate dynamical features of quantum systems corresponding to chaos (so called “quantum chaos”) with the origin of irreversibility. They are based on studying topological defects of phase in the Husimi representation. Dynamical process leading to random phase is found in “quantum chaos”. The role of this for the origin of irreversibility is discussed from the following two points: (i) phase retrieval problem; (ii) entanglement of phase defects.