• Statistical features of quantum evolution

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      https://www.ias.ac.in/article/fulltext/pram/073/02/0251-0257

    • Keywords

       

      $\mathcal{PT}$ symmetry; random matrix theory; time correlation functions.

    • Abstract

       

      It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian of the quantum system for an arbitrary pseudo-unitary (and hence $\mathcal{PT}$ -) quantum evolution. The result generalizes the time– energy uncertainty principle for pseudo-unitary quantum evolutions. Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that can be modelled by random matrix theory.

    • Author Affiliations

       

      Sudhir R Jain1

      1. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
    • Dates

       
  • Pramana – Journal of Physics | News

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