Aspects of coherent states of nonlinear algebras

2010/05/31 by T. Shreecharan, K. V. S. Shiv Chaitanya
Computer Science · Mathematics · Physics and Astronomy · #Coherent states #Coherent states in mathematical physics #Lagrangian coherent structures #Laplace transform #Mathematical functions and polynomials #Nonlinear system #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #State (computer science) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.3514118

published as J. Math. Phys. 51 (2010) 123511 · 22 Pages, 30 Figures

arxiv created 2010/05/31 · openalex publication_date 2010/12/01 · arxiv updated 2015/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Various aspects of coherent states of nonlinear su(2) and su(1, 1) algebras are studied. It is shown that the nonlinear su(1, 1) Barut–Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.

Citations

• Coherent states: Theory and some applications
• Appearance of Gauge Structure in Simple Dynamical Systems
• Geometric phases for generalized squeezed coherent states
• Group Theory and the Hydrogen Atom (II)
• Quantal phase factors accompanying adiabatic changes
• Beyond fuzzy spheres
• Group Theory and the Hydrogen Atom (I)