Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations
نویسندگان
چکیده
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 Chaturvedi et al (arXiv : 0706.0964 [quant-ph]). E-mail address : [email protected] E-mail address : [email protected] 1
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