Positivity Representations for Non-Hermitian Hamiltonians

Handy, Carlos R.

doi:10.1023/b:cjop.0000014368.29916.99

Czechoslovak Journal of Physics

2004

DOI: 10.1023/b:cjop.0000014368.29916.99

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Positivity Representations for Non-Hermitian Hamiltonians

Carlos R. Handy

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Cited by 4 publications

References 30 publications

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Experiments in PT-Symmetric Quantum Mechanics

Znojil

2004

Czechoslovak Journal of Physics

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Hill-determinant method is described and shown applicable within the so called PTsymmetric quantum mechanics. We demonstrate that in a way paralleling its traditional Hermitian applications and proofs the method guarantees the necessary asymptotic decrease of wave functions ψ(x) as resulting from a fine-tuned mutual cancellation of their asymptotically growing exponential components. Technically, the rigorous proof is needed/offered that in a quasi-variational spirit the method allows us to work, in its numerical implementations, with a sequence of truncated forms of the rigorous Hill-determinant power series for the normalizable bound states ψ(x).

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Experiments in PT-Symmetric Quantum Mechanics

Znojil

2004

Czechoslovak Journal of Physics

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Solvable PT-symmetric model with a tunable interspersion of nonmerging levels

Znojil

2005

Journal of Mathematical Physics

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We study the spectrum in such a PT −symmetric square well (of a diameter L ≤ ∞)where the "strength of the non-Hermiticity" is controlled by the two parameters, viz., by an imaginary coupling ig and by the distance ℓ < L of its onset from the origin. We solve this problem and confirm that the spectrum is discrete and real in a non-empty interval of g ≤ g 0 (ℓ, L). Surprisingly, a specific distinction between the bound states is found in their asymptotic stability/instability with respect to an unlimited growth of g beyond g 0 (ℓ, L). In our model, all of the low-lying levels remain asymptotically unstable at the small ℓ ≪ L and finite L while only the stable levels survive near ℓ ≈ L < ∞ or in the purely imaginary force limit with 0 < ℓ < L = ∞. In between these two extremes, an unusual and tunable, variable pattern of the interspersed "robust" and "fragile" subspectra of the real levels is obtained.PACS 03.65.Ge, 03.65.

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Effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong coupling

Yahiaoui¹,

Cherroud²,

Bentaiba³

2007

Journal of Mathematical Physics

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Positivity Representations for Non-Hermitian Hamiltonians

Cited by 4 publications

References 30 publications

Experiments in PT-Symmetric Quantum Mechanics

Experiments in PT-Symmetric Quantum Mechanics

Solvable PT-symmetric model with a tunable interspersion of nonmerging levels

Effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong coupling

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