An exactly solvable quantum-lattice model with a tunable degree of nonlocality

Miloslav Znojil (1)

1 Nuclear Physics Institute [Prague]

A non-Hermitian N −site-lattice Hamiltonian H with Laguerre-polynomial right eigenvectors and real energies is made self-adjoint in an ad hoc Hilbert space H (S). The necessary physical inner products are defined via alternative k−parametric (2k +1)−diagonal metrics Θ = Θ k constructed, in closed form, at k = 0, k = 1, k = 2 and k = 3. The value of k is interpreted as a degree of non-locality of the model.

Mots clés: Physical Sciences

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Miloslav Znojil. An exactly solvable quantum-lattice model with a tunable degree of nonlocality. Journal of Physics A: Mathematical and Theoretical, 2011, 44 (7), pp.075302. ⟨10.1088/1751-8113/44/7/075302⟩. ⟨hal-00789285⟩