Ray space `Riccati' evolution and geometric phases for 𝑁-level quantum systems
S Chaturvedi E Ercolessi G Marmo G Morandi N Mukunda R Simon
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We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group $\mathbb{U}(N)$ describing the Schrõdinger evolution of an 𝑁-level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in 𝑁-level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.
S Chaturvedi1 E Ercolessi2 G Marmo3 G Morandi4 N Mukunda5 R Simon6
Volume 96, 2022
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