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

Znojil, Miloslav

doi:10.1016/j.physleta.2007.03.010

Cited by 16 publications

(24 citation statements)

References 48 publications

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“…It remains for us to discuss the models with odd dimensions N = 2M+1, At a few higher M>4 we just re-confirmed the validity of the extrapolated formulae (18) by their insertion in secular equations.…”

Section: Odd Dimensions and The Test At N =supporting

confidence: 52%

“…Out of the generic three-by-three model of ref. [17] with two free parameters, 6 Four-dimensional model of paper [18] The four-dimensional model of paper [18] contains four free real parameters, but it contains our present two-parametric chain model with N = 3 as a special case. Such a reduction simplifies the N = 4 secular equation The discussion of the two-dimensional domain D (4) of the reality of these energies is entirely analogous to the previous case.…”

Section: Three-dimensional Model Of Paper [17]mentioning

confidence: 99%

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PT-symmetric Quantum Chain Models

Znojil¹

2007

Acta Polytech

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Section: Odd Dimensions and The Test At N =supporting

confidence: 52%

Section: Three-dimensional Model Of Paper [17]mentioning

confidence: 99%

PT-symmetric Quantum Chain Models

Znojil¹

2007

Acta Polytech

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“…We saw that once the real measure f 2 of the violation of self-duality becomes different from zero, our first nontrivial, up-down-asymmetric model (2) (skipped in [6] as complicated) offers a challenging eigenvalue problem. We have shown that its discussion and the non-numerical construction of its physical domain of parameters D still remains feasible and compact.…”

Section: Discussionmentioning

confidence: 99%

Conditional observability versus self-duality in a schematic model

Znojil¹

2008

J. Phys. A: Math. Theor.

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For a 4-dimensional 3-parametric toy Hamiltonian H(a, b, c) we construct the domain D of couplings in which the eigenvalues E n remain real (i.e., in principle, observable).A relationship is found between the reflection symmetry of the spectrum (i.e., its Dunne's and Shifman's self-duality E j = −E N +1−j at N = 4) and a geometric symmetry of the physical domain D. Simultaneously, both remain unbroken at a = c.

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“…Having skipped the N = 2 model as trivial, let us pick up, for illustration, the next, N = 4 example [19]. Once we reparametrize the Hamiltonian H…”

Section: Coupling Qc Regimementioning

confidence: 99%

“…The study of properties of the general N by N Hamiltonians H (N ) remains non-numerical up to the dimension N = 4, i.e., up to the secular polynomials of the fourth order (cf. [19]).…”

Section: Appendix a Crypto-hermitian Hamiltoniansmentioning

confidence: 99%

Quantum catastrophes: a case study

Znojil¹

2012

J. Phys. A: Math. Theor.

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The bound-state spectrum of Hamiltonian H = H(λ) is assumed real in a non-empty domain of multiindex λ ∈ D (physical) . The name of quantum catastrophe (QC) is introduced for the scenario in which λ leaves this domain in such a manner that an N−plet of the bound state energies degenerates at the boundary ∂D (physical) and, subsequently, complexifies. Our benchmark version of the QC scenario uses a family of crypto-Hermitian N by N matrices H (N ) (λ). Up to the very QC horizon ∂D (physical) the explicit construction of the standard physical ad hoc Hilbert space H (S) = H (S) (λ) (i.e., of a hermitizing metric Θ = Θ (N ) (λ)) is simplified and shown feasible at any N.

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

Cited by 16 publications

References 48 publications

PT-symmetric Quantum Chain Models

PT-symmetric Quantum Chain Models

Conditional observability versus self-duality in a schematic model

Quantum catastrophes: a case study

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