Tridiagonal PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

0092533 - ÚJF 2008 RIV GB eng J - Journal Article
Znojil, Miloslav
Tridiagonal PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime.
[Tridiagonal PT-symmetrický N-by-N Hamiltonians.]
Journal of Physics A-Mathematical and Theoretical. Roč. 40, č. 43 (2007), s. 13131-13148. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA MŠMT LC06002; GA ČR GA202/07/1307
Institutional research plan: CEZ:AV0Z10480505
Keywords : quantum-mechanics * pseudo-hermiticity * anharmonic-oscillators
Subject RIV: BE - Theoretical Physics
Impact factor: 1.680, year: 2007

A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N < infinity dimensions, H -> H-(chain model), and all its up-down symmetrized special cases with J = [N/2] real couplings are considered, H-(chain model) -> H-(N). Using symbolic manipulation and extrapolation techniques we find out that in the strongly non-Hermitian regime the secular equation gets partially factorized at all N. This enables us to reveal a fine-tuned alignment of the dominant couplings implying an asymptotically sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity domain D-(N) in which all the spectrum of energies E-n((N)) remains real and observable.

Tridiagonal PT-symmetrický N-by-N Hamiltonians.
Permanent Link: http://hdl.handle.net/11104/0152827