• Ray space `Riccati' evolution and geometric phases for 𝑁-level quantum systems

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/069/03/0317-0327

• # Keywords

Quantum dynamics; Riccati equations; geometric phase.

• # Abstract

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.

• # Author Affiliations

2. Physics Department, University of Bologna, CNISM and INFN, 46 v.Irnerio, I-40126, Bologna, Italy
3. Dipartimento di Scienze Fisiche, University of Napoli and INFN, v.Cinzia, I-80126, Napoli, Italy
4. Physics Department, University of Bologna, CNISM and INFN, 6/2 v.le Berti Pichat, I-40127, Bologna, Italy
5. Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
6. The Institute of Mathematical Sciences, C.I.T Campus, Chennai 600 113, India

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019