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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

SYSNO ASEP	0333958
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Author(s)	Znojil, Miloslav (UJF-V)_{RID, ORCID, SAI}
Source Title	Symmetry, Integrability and Geometry: Methods and Applications. - : Natsional'na Akademiya Nauk Ukrainy - ISSN 1815-0659 Roč. 5, - (2009), 085/1-085/21
Number of pages	21 s.
Language	eng - English
Country	UA - Ukraine
Keywords	cryptohermitian observables ; unitary scattering ; Runge-Kutta discretization
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)
UT WOS	000271092200021
DOI	10.3842/SIGMA.2009.085
Annotation	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.
Workplace	Nuclear Physics Institute
Contact	Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228
Year of Publishing	2010

Number of the records: 1