Solitons in the Calogero-Sutherland collective-field model

Andrié, I; Bardek, V.; Jonke, Larisa

doi:10.1016/0370-2693(95)00910-d

Cited by 29 publications

(32 citation statements)

References 14 publications

(14 reference statements)

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“…It has already been obtained in the collective-field approach to the one-family Calogero model [18,20]. The second-family lump solution transforms into the sharp deltafunction profileρ…”

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confidence: 86%

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Solitons in the Calogero model for distinguishable particles

Bardek

Meljanac

2005

Europhys. Lett.

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We consider a large −N, two-family Calogero model in the Hamiltonian, collectivefield approach. The Bogomol'nyi limit appears and the corresponding solutions are given by the static-soliton configurations. Solitons from different families are localized at the same place. They behave like a paired hole and lump on the top of the uniform vacuum condensates, depending on the values of the coupling strengths.When the number of particles in the first family is much larger than that of the second family, the hole solution goes to the vortex profile already found in the onefamily Calogero model.

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“…It has already been obtained in the collective-field approach to the one-family Calogero model [18,20]. The second-family lump solution transforms into the sharp deltafunction profileρ…”

mentioning

confidence: 86%

“…Our final remark is that our two-family Calogero model without the three-body interaction (18) can be viewed as the one-family model, but only in the leading approximation. Namely, comparing the effective potential (15) with the effective potential for the one-family Calogero model, one finds that they can be identified.…”

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confidence: 99%

Solitons in the Calogero model for distinguishable particles

Bardek

Meljanac

2005

Europhys. Lett.

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“…Nonlocal interactions also occur in optical systems, such as those mediated by thermal conduction [45][46][47][48][49], and their consequences have been observed experimentally [50,51]. The CS model is integrable and hence supports true solitons [52][53][54][55], whereas non-neutral plasmas are not integrable systems and only support solitary waves. Dipolar BECs display an instability where the attractive part of the interaction can cause the system to collapse [40]; far from the instability solitary waves are predicted to collide elastically and thus behave as solitons, whereas close to the instability the collisions become inelastic due to the emission of phonons [56].…”

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confidence: 95%

Balancing long-range interactions and quantum pressure: Solitons in the Hamiltonian mean-field model

Plestid

O’Dell

2019

Phys. Rev. E

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The Hamiltonian Mean Field (HMF) model describes particles on a ring interacting via a cosine interaction, or equivalently, rotors coupled by infinite-range XY interactions. Conceived as a generic statistical mechanical model for long-range interactions such as gravity (of which the cosine is the first Fourier component), it has recently been used to account for self-organization in experiments on cold atoms with long-range optically mediated interactions. The significance of the HMF model lies in its ability to capture the universal effects of long-range interactions and yet be exactly solvable in the canonical ensemble. In this work we consider the quantum version of the HMF model in 1D and provide a classification of all possible stationary solutions of its generalized Gross-Pitaevskii equation (GGPE) which is both nonlinear and nonlocal. The exact solutions are Mathieu functions that obey a nonlinear relation between the wavefunction and the depth of the meanfield potential, and we identify them as bright solitons. Using a Galilean transformation these solutions can be boosted to finite velocity and are increasingly localized as the meanfield potential becomes deeper. In contrast to the usual local GPE, the HMF case features a tower of solitons, each with a different number of nodes. Our results suggest that long-range interactions support solitary waves in a novel manner relative to the short-range case.

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“…The periodic and nonperiodic solutions of Eq. (38) were already found in [15][16][17][18]. For example, the nonperiodic soliton solution reads…”

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confidence: 80%