Počet záznamů: 1

Gegenbauer-solvable quantum chain model

  1. 1.
    0350891 - UJF-V 2011 RIV US eng J - Článek v odborném periodiku
    Znojil, Miloslav
    Gegenbauer-solvable quantum chain model.
    Physical Review. A. Roč. 82, č. 5 (2010), 052113/1-052113/10 ISSN 1050-2947
    Grant CEP: GA MŠk LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: NON-HERMITIAN HAMILTONIANS * PSEUDO-HERMITICITY * FIELD-THEORY
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 2.861, rok: 2010

    An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n, a, x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H not equal H-dagger. We managed to (i) start from elementary secular equation G(N, a, E-n) = 0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Theta not equal I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice.
    Trvalý link: http://hdl.handle.net/11104/0190769