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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
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SYSNO ASEP 0333958 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators Tvůrce(i) Znojil, Miloslav (UJF-V) RID, ORCID, SAI Zdroj.dok. Symmetry, Integrability and Geometry: Methods and Applications. - : Natsional'na Akademiya Nauk Ukrainy - ISSN 1815-0659
Roč. 5, - (2009), 085/1-085/21Poč.str. 21 s. Jazyk dok. eng - angličtina Země vyd. UA - Ukrajina Klíč. slova cryptohermitian observables ; unitary scattering ; Runge-Kutta discretization Vědní obor RIV BE - Teoretická fyzika CEP LC06002 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy GA202/07/1307 GA ČR - Grantová agentura ČR CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000271092200021 DOI 10.3842/SIGMA.2009.085 Anotace One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H not equal H-dagger is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv: 0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Theta not equal I represented, in Runge-Kutta approximation, by (2R-1)-diagonal matrices. Pracoviště Ústav jaderné fyziky Kontakt Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Rok sběru 2010
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