Comment on: “Comparison of quantal and classical behavior of PT-symmetric systems at avoided crossings” [Phys. Lett. A 334 (2005) 144]

Bíla, Hynek; Tater, Miloš; Znojil, Miloslav

doi:10.1016/j.physleta.2006.01.004

Cited by 9 publications

(21 citation statements)

References 1 publication

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“…For illustration we may recollect an electron in a critically strong field where the single-particle Dirac equation must necessarily be replaced by its field-theoretical extension including many new degrees of freedom [25]. In a related brief comment [26] we emphasized that even on the level of the practical analyses of quantum systems using some oversimplified phenomenological models it is not always easy to draw the clear separation line between the avoided and unavoided level crossings. A reliable separation of the two seem strongly model-dependent at present.…”

Section: Construction Of the Surface ∂D Near The Nonperturbative Pmn mentioning

confidence: 99%

Determination of the domain of the admissible matrix elements in the four-dimensional -symmetric anharmonic model

Znojil

2007

Physics Letters A

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Section: Construction Of the Surface ∂D Near The Nonperturbative Pmn mentioning

confidence: 99%

Determination of the domain of the admissible matrix elements in the four-dimensional -symmetric anharmonic model

Znojil

2007

Physics Letters A

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“…In the last years there has been great interest in the properties of PTsymmetric multidimensional oscillators [1][2][3][4][5][6][7][8][9]. Among them we mention the complex versions of the Barbanis [1, 2, 4-6, 8, 9] and Hénon-Heiles [1,6] Hamiltonians.…”

Section: Introductionmentioning

confidence: 99%

Is space-time symmetry a suitable generalization of parity-time symmetry?

Amore¹,

Fernández²,

García³

2014

Annals of Physics

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We discuss space-time symmetric Hamiltonian operators of the form H = H 0 +igH ′ , where H 0 is Hermitian and g real. H 0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G ′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < g c , where g c is the exceptional point closest to the origin.Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two-and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.

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“…Recently Asiri Nanayakkara formulated an "inverse problem" and studied certain specific systems, which exhibit chaotic behaviour on the classical level. Our comment [12], based on a sophisticated numerical analysis, re-evaluated his quantum results and clarified that his numerical observations of a correspondence between classical chaos and quantum phenomenon of level crossing, may be (and probably is) just an effect of an insufficient numerical precision of his calculations.…”

Section: Consequences Of the Formalism In Some Other Branches Of Quanmentioning

confidence: 79%

“…by our recent letter [12]. It encouraged our persuasion that between the ordinary and partial differential forms of observables there might exist a broad space for their representations of an "intermediate complexity" possessing a differential-difference (or, in the language of physics, channel-coupling) structure.…”

Section: The Case Of Two Commuting Nonhermitian Observablesmentioning

confidence: 99%