Pramana | |
Ray space `Riccati' evolution and geometric phases for ð?‘?-level quantum systems | |
E Ercolessi21  R Simon4  G Marmo6  G Morandi5  N Mukunda3  S Chaturvedi2  | |
[1] Physics Department, University of Bologna, CNISM and INFN, 46 v.Irnerio, I-40126, Bologna, Italy$$;School of Physics. University of Hyderabad, Hyderabad 500 046, India$$;Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India$$;The Institute of Mathematical Sciences, C.I.T Campus, Chennai 600 113, India$$;Physics Department, University of Bologna, CNISM and INFN, 6/2 v.le Berti Pichat, I-40127, Bologna, Italy$$;Dipartimento di Scienze Fisiche, University of Napoli and INFN, v.Cinzia, I-80126, Napoli, Italy$$ | |
关键词: Quantum dynamics; Riccati equations; geometric phase.; | |
DOI : | |
学科分类:物理(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
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 ð‘-level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in ð‘-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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040497362ZK.pdf | 137KB | download |