Quantum innerproduct metrics via the recurrent solution of the Dieudonné equation
Abstract
A given Hamiltonian matrix H with a real spectrum is assumed tridiagonal and nonHermitian, H ≠ H†. Its possible Hermitizations via an amended, ad hoc innerproduct metric Θ = Θ† > 0 are studied. Under certain reasonable assumptions, all of these metrics Θ = Θ(H) are shown to be obtainable as recurrent solutions of the hidden Hermiticity constraint H† Θ = Θ H called the Dieudonné equation. In this framework, even the twoparametric Jacobipolynomial real and asymmetric Nsite lattice H^{(N)}(μ, ν) is found to be exactly solvable at all N.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2012
 DOI:
 10.1088/17518113/45/8/085302
 arXiv:
 arXiv:1201.2263
 Bibcode:
 2012JPhA...45h5302Z
 Keywords:

 Mathematical Physics;
 Quantum Physics
 EPrint:
 21 pp