Quantum Signatures of Breather-Breather Interactions

Dorignac, Jérôme; Eilbeck, J. C.; Salerno, Mario; Scott, Alwyn C.

doi:10.1103/physrevlett.93.025504

Cited by 55 publications

(68 citation statements)

References 19 publications

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“…In many cases quantum dynamics is important. Quantum breathers consist of superpositions of nearly degenerate many-quanta bound states, with very long times to tunnel from one lattice site to another [4,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Remarkably quantum breathers, though being extended states in a translationally invariant system, are characterized by exponentially localized weight functions, in full analogy to their classical counterparts.…”

Section: Introductionmentioning

confidence: 99%

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

2007

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We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended states in the normal mode space of the noninteracting system. Weight functions of the eigenstates in the space of normal modes are computed by using numerical diagonalization and perturbation theory. We find that staggered states do not compactify in the dilute limit for large chains.

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Section: Introductionmentioning

confidence: 99%

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

2007

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“…Eq. (18) shows that the survival probability supports a high frequency modulation whose amplitude decreases with ǫ. Such a modulation, whose frequency is equal to the energy difference between |n, 0 and |n, 1 , characterizes the small participation of the second band in the dynamics.…”

Section: Application To V = 2 and V =mentioning

confidence: 87%

“…Therefore, the corresponding eigenstates cannot localize the energy because they must share the symmetry of the translation operator which commutes with the lattice Hamiltonian. Nevertheless, the nonlinearity is responsible for the occurrence of specific states called multi-quanta bound states [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. A bound state corresponds to the trapping of several quanta over only a few neighbouring sites, with a resulting energy which is less than the energy of quanta lying far apart.…”

Section: Introductionmentioning

confidence: 99%

Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice

Falvo

Pouthier

Eilbeck

2006

Physica D: Nonlinear Phenomena

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By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown that the creation of v quanta on one site excites a soliton band formed by bound states involving v quanta trapped on the same site. The energy is first localized on the excited site over a significant timescale and then slowly delocalizes along the lattice. As when increasing the nonlocal nonlinearity, a faster dynamics occurs and the energy propagates more rapidly along the lattice. Nevertheless, the larger is the number of quanta, the slower is the dynamics. However, it is shown that when the nonlocal nonlinearity reaches a critical value, the lattice suddenly supports a very fast energy propagation whose dynamics is almost independent on the number of quanta. The energy is transfered by specific bound states formed by the superimposition of states involving v − p quanta trapped on one site and p quanta trapped on the nearest neighbour sites, with p = 0, .., v − 1. These bound states behave as independent quanta and they exhibit a dynamics which is insensitive to the nonlinearity and controlled by the single quantum hopping constant.

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“…Standing breathers correspond to localized solutions whose amplitudes vary in time. The exactly solvable sine-Gordon equation [23,24] and the focusing nonlinear Schrödinger equation [25,26] are examples of one-dimensional partial differential equations that possess breather solutions. In Fig.…”

Section: P T T Q T T ζ ζ η ηmentioning

confidence: 99%

Exact solutions and excitations for the Davey-Stewartson equations with nonlinear and gain terms

Wang

Huang

2010

Eur. Phys. J. D

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Abstract AbstractWe study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS equations, and further demonstrate different features of these excitations. More importantly, the similar solutions and excitations can be predicted to exist in other related revolution equations such as nonlinear Schrödinger equation to explain the Bose-Einstein condensation.

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Quantum Signatures of Breather-Breather Interactions

Cited by 55 publications

References 19 publications

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice

Exact solutions and excitations for the Davey-Stewartson equations with nonlinear and gain terms

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