Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations

Abstract

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).

Latex ; 13 pages ; no figure

References in corpus (3)

• A nonlinear superposition rule for solutions of the Milne--Pinney equation
• Quantum Hall Effect on the Flag Manifold F_2
• Ray space Riccati evolution and geometric phases for N-level quantum systems

Cited by in corpus (4)

• Riccati Diagonalization of Hermitian Matrices
• A Geometric Parametrization of the Cabibbo-Kobayashi-Maskawa Matrix and the Jarlskog Invariant
• SO(2N)/U(N) Riccati-Hartree-Bogoliubov Equation Based on the SO(2N) Lie Algebra of the Fermion Operators
• Canonical form of the Evolution Operator of a Time-Dependent Hamiltonian in the Three Level System