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Tridiagonal PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
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SYSNO ASEP 0092533 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Tridiagonal PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime Title Tridiagonal PT-symmetrický N-by-N Hamiltonians Author(s) Znojil, Miloslav (UJF-V) RID, ORCID, SAI Source Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 40, č. 43 (2007), s. 13131-13148Number of pages 18 s. Language eng - English Country GB - United Kingdom Keywords quantum-mechanics ; pseudo-hermiticity ; anharmonic-oscillators Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GA202/07/1307 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10480505 - UJF-V (2005-2011) Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2008
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