Quantum inner-product metrics via recurrent solution of Dieudonne equation

Details Quantum inner-product metrics via recurrent solution of Dieudonne equation Quantum inner-product metrics via recurrent solution of Dieudonne equation

2012-01-11

arxiv.org/abs/1201.2263v1

J. Phys. A: Math. Theor. 45 (2012) 085302

Physics

Mathematical Physics

21 pp

Scientific paper

10.1088/1751-8113/45/8/085302

A given Hamiltonian matrix H with real spectrum is assumed tridiagonal and non-Hermitian. Its possible Hermitizations via an amended, ad hoc inner-product metric are studied. Under certain reasonable assumptions, all of these metrics are shown obtainable as recurrent solutions of the hidden Hermiticity constraint called Dieudonne equation. In this framework even the two-parametric Jacobi-polynomial real- and asymmetric-matrix N-site lattice Hamiltonian is found tractable non-numerically at all N.

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