2019/08/09 by K. S. Akhilesh, Akhilesh, K S, Arvind Arvind +7 · 1 citation
Chemistry · Physics and Astronomy · Mathematics · #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics #Algebraic structures and combinatorial models
paper · doi:10.48550/arxiv.1908.03325
We present a study of the properties of Bargmann Invariants (BI) and Null Phase Curves (NPC) in the theory of the geometric phase for finite dimensional systems. A recent suggestion to exploit the Majorana theorem on symmetric SU(2) multispinors is combined with the Schwinger oscillator operator construction to develop efficient operator based methods to handle these problems. The BI is described using intrinsic unitary invariant angle parameters, whose algebraic properties as functions of Hilbert space dimension are analysed using elegant group theoretic methods. The BI-geometric phase connection, extended by the use of NPC's, is explored in detail, and interesting new experiments in this subject are pointed out.