• Analytic representations with theta functions for systems on ℤ(d) and on 𝕊.

      Evangelides, Pavlos; Lei, Ci; Vourdas, Apostolos (2015-07-28)
      An analytic representation with Theta functions on a torus, for systems with variables in ℤ(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied.
    • Paths of zeros of analytic functions describing finite quantum systems.

      Eissa, Hend A.; Evangelides, Pavlos; Lei, Ci; Vourdas, Apostolos (2016-02-05)
      Quantum systems with positions and momenta in Z(d) are described by the d zeros of analytic functions on a torus. The d paths of these zeros on the torus describe the time evolution of the system. A semi-analytic method for the calculation of these paths of the zeros is discussed. Detailed analysis of the paths for periodic systems is presented. A periodic system which has the displacement operator to a real power t, as time evolution operator, is studied. Several numerical examples, which elucidate these ideas, are presented.