Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups

Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups

The development of efficient time optimal control strategies for coupled spin systems plays a fundamental role in nuclear magnetic resonance (NMR) spectroscopy. In particular, one of the major challenges lies in steering a given spin system to a maximum of its so-called transfer function. In this paper we study in detail these questions for a system of two weakly coupled spin-12 particles. Firs...

Probability on Compact Lie Groups

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Lie groups as spin groups

Abstract. It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available to simplify the analysis and applications of Lie groups and Lie algebras. The spin version of the general linear group is thoroughly analyzed, and an invariant method for constructing real...

Towards coordination algorithms on compact Lie groups

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so-called consensus state without using any external reference. In the same line of thought, a leader-follower approach where ’follower’ agents would track one ’leader’ agent is excluded, in fav...