SU(1,1) group action and the corresponding Bloch equation
Andrzej Okninski
TL;DR
This paper investigates discrete time dynamics on the SU(1,1) group, linking it to a Bloch equation, and provides exact solutions revealing dynamics similar to SU(2) Bloch behavior.
Contribution
It introduces a novel analysis of SU(1,1) group dynamics and connects it to a Bloch equation with exact solutions, highlighting similarities to SU(2) dynamics.
Findings
Exact solutions of the SU(1,1) map elucidate the dynamics.
Elliptic case dynamics resemble SU(2) Bloch dynamics.
Discrete time dynamics on SU(1,1) are characterized and analyzed.
Abstract
Discrete time dynamics on the SU(1,1) group is studied. It is shown that a map acting in the dual space is the stroboscopic map for a SU(1,1) Bloch equation. Exact solution of the map is used to elucidate the corresponding dynamics. It is shown that dynamics of the SU(1,1) Bloch equation in the elliptic case bears close analogy to the SU(2) Bloch dynamics.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Quantum and Classical Electrodynamics · Algebraic and Geometric Analysis