Ray space `Riccati' evolution and geometric phases for ð?‘?-level quantum systems

Pramana

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 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.

【 授权许可】

Unknown