Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations

Abstract

We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $s{u}_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.

LaTex file, 13 pages, 3 figures

References in corpus (4)

• An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models
• On the spectrum of a Hamiltonian defined on su_q(2) and quantum optical models
• Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models
• Symmetry as a source of hidden coherent structures in quantum physics: general outlook and examples

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• Exact solutions for a family of spin-boson systems
• Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems
• Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
• Exact ground-state correlation functions of an atomic-molecular boson conversion model
• Exact solution for a class of quantum models of interacting bosons
• Exact State Evolution and Energy Spectrum in Solvable Bosonic Models