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      Permanent link:
      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

       

      S Chaturvedi1 E Ercolessi2 G Marmo3 G Morandi4 N Mukunda5 R Simon6

      1. School of Physics. University of Hyderabad, Hyderabad 500 046, India
      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

    • Dates

       
      Published
      September 2007
      Manuscript received
      7 June 2007
      Manuscript revised
      3 July 2007
      Accepted
      6 July 2007

  • Pramana – Journal of Physics | News

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