About: Fundamental length in quantum theories with PT-symmetric Hamiltonians

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	One-dimensional motion of a quantum point particle is usually described by its wave function Sigma(x), where the argument x is an element of R represents a (measurable) coordinate and where the integrated probability density is normalized to one, integral Sigma()(x)Sigma(x)=1. The direct observability of x may be lost in PT-symmetric quantum mechanics where a %22smeared%22 metric kernel Theta(')((x,x))not equal delta(x-x(')) may enter the double-integral normalization Sigma()(x)Theta(')((x,x))Sigma(x('))=1. We argue that such a formalism proves particularly suitable for the introduction of a nonvanishing fundamental length theta > 0, which would characterize the %22smearing width%22 of the kernel Theta(')((x,x)). The technical feasibility of such a project is illustrated via a toy family of Hamiltonians H-(N)(lambda) taken from Ref. 11. For each element of this family the complete set of all the eligible metric kernels Theta(')((x,x))((N))(lambda) is constructed in closed form. One-dimensional motion of a quantum point particle is usually described by its wave function Sigma(x), where the argument x is an element of R represents a (measurable) coordinate and where the integrated probability density is normalized to one, integral Sigma()(x)Sigma(x)=1. The direct observability of x may be lost in PT-symmetric quantum mechanics where a %22smeared%22 metric kernel Theta(')((x,x))not equal delta(x-x(')) may enter the double-integral normalization Sigma()(x)Theta(')((x,x))Sigma(x('))=1. We argue that such a formalism proves particularly suitable for the introduction of a nonvanishing fundamental length theta > 0, which would characterize the %22smearing width%22 of the kernel Theta(')((x,x)). The technical feasibility of such a project is illustrated via a toy family of Hamiltonians H-(N)(lambda) taken from Ref. 11. For each element of this family the complete set of all the eligible metric kernels Theta(')((x,x))((N))(lambda) is constructed in closed form. (en)
Title	Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians (en)
skos:prefLabel	Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians (en)
skos:notation	RIV/61389005:_____/09:00333963!RIV10-MSM-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA202/07/1307), P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Znojil, Miloslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	315730
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/09:00333963
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	non-Hermitian Hamiltonians; anharmonic-oscillators; noncommutative space (en)
http://linked.open.../riv/klicoveSlovo	noncommutative space non-Hermitian Hamiltonians anharmonic-oscillators
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[F9FE08CB00CA]
http://linked.open...i/riv/nazevZdroje	Physical Review D: Particles, Fields, Gravitation and Cosmology
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics PT symmetry, supersymmetry and solvable models
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	80
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav
http://linked.open...ain/vavai/riv/wos	000269641400105
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	1550-7998
number of pages	20 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians Fundamental length in quantum theories with PT-symmetric Hamiltonians

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