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arXiv:1601.06586 · Physics Letters A

Paths of zeros of analytic functions describing finite quantum systems

Hend Abdelgader Eissa, Pavlos Evangelides, Chao Lei, Apostol Vourdas

Published Dec 2, 2015• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.11.032

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Finite quantum systems with d-dimension Hilbert space, where position x and \nmomentum p take values in Zd(the integers modulo d) are studied. An analytic \nrepresentation of finite quantum systems, using Theta function is considered. \nThe analytic function has exactly d zeros. The d paths of these zeros on the \ntorus describe the time evolution of the systems. The calculation of these \npaths of zeros, is studied. The concepts of path multiplicity, and path winding \nnumber, are introduced. Special cases where two paths join together, are also \nconsidered. A periodic system which has the displacement operator to real \npower t, as time evolution is also studied. \nThe Bargmann analytic representation for infinite dimension systems, with \nvariables in R, is also studied. Mittag-Leffler function are used as examples of \nBargmann function with arbitrary order of growth. The zeros of polynomial \napproximations of the Mittag-Leffler function are studied.