dorsal/arxiv
View SchemaLarge-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian
| Authors | Carl M. Bender, Gerald V. Dunne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812039 |
| URL | https://arxiv.org/abs/quant-ph/9812039 |
| DOI | 10.1063/1.532991 |
| Journal | J.Math.Phys. 40 (1999) 4616-4621 |
Abstract
A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian $H=p^2+{1/4}x^2+i \lambda x^3$, is performed using high-order Rayleigh-Schr\"odinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. The Rayleigh-Schr\"odinger perturbation series is Borel summable, and Pad\'e summation provides excellent agreement with the real energy spectrum. Pad\'e analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of $\lambda^2$ is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon x^3$.
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"abstract": "A precise calculation of the ground-state energy of the complex PT-symmetric\nHamiltonian $H=p^2+{1/4}x^2+i \\lambda x^3$, is performed using high-order\nRayleigh-Schr\\\"odinger perturbation theory. The energy spectrum of this\nHamiltonian has recently been shown to be real using numerical methods. The\nRayleigh-Schr\\\"odinger perturbation series is Borel summable, and Pad\\\u0027e\nsummation provides excellent agreement with the real energy spectrum. Pad\\\u0027e\nanalysis provides strong numerical evidence that the once-subtracted\nground-state energy considered as a function of $\\lambda^2$ is a Stieltjes\nfunction. The analyticity properties of this Stieltjes function lead to a\ndispersion relation that can be used to compute the imaginary part of the\nenergy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\\epsilon\nx^3$.",
"arxiv_id": "quant-ph/9812039",
"authors": [
"Carl M. Bender",
"Gerald V. Dunne"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th"
],
"doi": "10.1063/1.532991",
"journal_ref": "J.Math.Phys. 40 (1999) 4616-4621",
"title": "Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian",
"url": "https://arxiv.org/abs/quant-ph/9812039"
},
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