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      https://www.ias.ac.in/article/fulltext/pram/045/06/0471-0497

    • Keywords

       

      Symplectic groups; symplectic geometry; Huyghens kernel; uncertainty principle; multimode squeezing; Gaussian states

    • Abstract

       

      We present a utilitarian review of the family of matrix groups Sp(2n, ℛ), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n, ℛ). Global decomposition theorems, interesting subgroups and their generators are described. Turning ton-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n, ℛ) action are delineated.

    • Author Affiliations

       

      Arvind1 B Dutta1 2 N Mukunda1 2 3 R Simon1 4

      1. Department of Physics, Indian Institute of Science, Bangalore - 560 012, India
      2. Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore - 560 064, India
      3. Centre for Theoretical Studies and Department of Physics, Indian Institute of Science, Bangalore - 560 012, India
      4. Institute of Mathematical Sciences, C. I. T. Campus, Madras - 600 113, India
    • Dates

       
  • Pramana – Journal of Physics | News

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