2015
DOI: 10.1007/s10773-014-2467-0
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Supersymmetric Model of a Bose-Einstein Condensate in a 𝓟𝓣-Symmetric Double-delta Trap

Abstract: The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external PT -symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the PT -symmetric as well as in the PT -broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the sin… Show more

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Cited by 14 publications
(13 citation statements)
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“…One speaks of broken PT symmetry, and the EP marks the position of the PT symmetry breaking. Since the occurrence of exceptional points is a generic feature of the PT phase transition a large number of works exists for PT -symmetric quantum mechanics [27,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], quantum field theories [50,51], electromagnetic waves [52][53][54][55][56][57][58], and electronic devices [59].…”
Section: Introductionmentioning
confidence: 99%
“…One speaks of broken PT symmetry, and the EP marks the position of the PT symmetry breaking. Since the occurrence of exceptional points is a generic feature of the PT phase transition a large number of works exists for PT -symmetric quantum mechanics [27,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], quantum field theories [50,51], electromagnetic waves [52][53][54][55][56][57][58], and electronic devices [59].…”
Section: Introductionmentioning
confidence: 99%
“…In quantum systems their existence has been proved in atomic [13][14][15][16] or molecular [17] spectra, in the scattering of particles at potential barriers [18], in atom waves [19][20][21][22], and in non-Hermitian Bose-Hubbard models [23]. Their relation to Fano resonances has been pointed out [24][25][26].…”
Section: Introductionmentioning
confidence: 99%
“…Examples for theoretical treatments of EPs in quantum systems are atomic [5][6][7][8] and molecular [9,10] spectra, scattering of particles at potential barriers [11,12], atom waves [13][14][15][16], open Bose-Hubbard systems [17], unstable lasers [18], resonators [19], and optical waveguides [20,21]. Furthermore there exists experimental evidence of EPs.…”
Section: Introductionmentioning
confidence: 99%
“…or in SI unitsF EP ≡ 1.633 870 × 10 8 V/m, B EP ≡ 3.396 368 × 10 3 T,(15)which leads to coalescence at the eigenvalue E EP = −2.703 665 × 10 −2 − 4.171 979 × 10 −4 i (16). …”
mentioning
confidence: 99%