Quantum inner-product metrics via recurrent solution of Dieudonne equation
arXiv:1201.2263 · doi:10.1088/1751-8113/45/8/085302
Abstract
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.
21 pp
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- Anomalous mechanisms of the loss of observability in non-Hermitian quantum models
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- Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
- Broken Hermiticity phase transition in Bose-Hubbard model
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