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Gegenbauer-solvable quantum chain model
- 1.0350891 - ÚJF 2011 RIV US eng J - Journal Article
Znojil, Miloslav
Gegenbauer-solvable quantum chain model.
Physical Review. A. Roč. 82, č. 5 (2010), 052113/1-052113/10. ISSN 1050-2947
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : NON-HERMITIAN HAMILTONIANS * PSEUDO-HERMITICITY * FIELD-THEORY
Subject RIV: BE - Theoretical Physics
Impact factor: 2.861, year: 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.
Permanent Link: http://hdl.handle.net/11104/0190769
Number of the records: 1