Transition states and thermal collapse of dipolar Bose-Einstein condensates

Junginger, Andrej; Kreibich, Manuel; Main, Jörg

doi:10.1103/physreva.88.043617

Cited by 9 publications

(16 citation statements)

References 34 publications

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“…The rate is obtained from the flux through the DS and it is exact if and only if the DS is free of recrossings. Advances in the determination of this fundamental quantity can impact a broad range of problems in atomic physics [19], solid state physics [20], cluster formation [21,22], diffusion dynamics [23,24], cosmology [25], celestial mechanics [26,27], and Bose-Einstein condensates [28][29][30][31][32], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Feldmaier

Junginger

Main

et al. 2017

Chemical Physics Letters

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Dynamics between reactants and products are often mediated by a rate-determining barrier and an associated dividing surface leading to the transition state theory rate. This framework is challenged when the barrier is time-dependent because its motion can give rise to recrossings across the fixed dividing surface. A non-recrossing time-dependent dividing surface can neverthless be attached to the TS trajectory resulting in recrossing-free dynamics. We extend the formalism -contstructed using Lagrangian Descriptors-to systems with additional bath degrees of freedom. The propagation of reactant ensembles provides a numerical demonstration that our dividing surface is recrossing-free and leads to exact TST rates.

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Section: Introductionmentioning

confidence: 99%

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Feldmaier

Junginger

Main

et al. 2017

Chemical Physics Letters

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“…Any lower density would result in an excited but stable BEC. This interpretation can be verified by actually calculating the dynamics of the BEC [28,41], which reveals its collapse in the center of the trap after the transition state has been crossed.…”

Section: Becs With Short-range Interactionmentioning

confidence: 72%

“…In this paper, we investigate the thermal decay of condensates at low temperatures T in the region 0 < T 0 < T T c , i. e. above a temperature T 0 ∼ ω/k B where col-lective oscillations with frequency ω are thermally excited and significantly below the critical temperature T c where the macroscopic occupation of the ground state sets in. In that temperature regime, the thermal excitations of the condensate are of collective nature and single-particle excitations can be neglected [27,28]. In addition, three-body collisions due to high condensate densities do not influence the decay rate corresponding to the thermally induced coherent collapse, because they only become important after the transition state has been crossed.…”

Section: Introductionmentioning

confidence: 99%

Normal form expansions and thermal decay rates of Bose-Einstein condensates with short- and long-range interaction

et al. 2015

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The thermally induced coherent collapse of Bose-Einstein condensates at finite temperature is the dominant decay mechanism near the critical scattering length in condensates with at least partially attractive interaction. The collapse dynamics out of the ground state is mediated by a transition state whose properties determine the corresponding decay rate or lifetime of the condensate. In this paper, we perform normal form expansions of the ground and the transition state of condensates with shortrange scattering interaction as well as with anisotropic and long-range dipolar interaction in a variational framework. This method allows one to determine the local properties of these states, i. e. their mean-field energy, their normal modes, the coupling between different modes, and the structure of the reaction channel to any desired order. We discuss the physical interpretation of the transition state as a certain density distribution of the atomic cloud and the behavior of the single normal form contributions in dependence on the s-wave scattering length. Moreover, we investigate the convergence of the local normal form when using extended Gaussian variational approaches, and present the condensate's decay rate.PACS. 67.85.De -03.75.Kk arXiv:1411.0458v3 [cond-mat.quant-gas]

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“…can also be written as H = Ĥ − µN , (2.92) which defines the system chemical potential 93) in which the condensate fraction and the fraction of uncondensed particles are…”

Section: Thermodynamic Characteristicsmentioning

confidence: 99%

Dipolar and spinor bosonic systems

Yukalov

2018

Laser Phys.

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The main properties and methods of describing dipolar and spinor atomic systems, composed of bosonic atoms or molecules, are reviewed. The general approach for the correct treatment of Bose-condensed atomic systems with nonlocal interaction potentials is explained. The approach is applied to Bose-condensed systems with dipolar interaction potentials. The properties of systems with spinor interaction potentials are described. Trapped atoms and atoms in optical lattices are considered. Effective spin Hamiltonians for atoms in optical lattices are derived. The possibility of spintronics with cold atom is emphasized. The present review differs from the previous review articles by concentrating on a thorough presentation of basic theoretical points, helping the reader to better follow mathematical details and to make clearer physical conclusions.Cold atomic and molecular bosonic systems have recently been the objects of intensive research, both experimental and theoretical. First, the attention has been concentrated on dilute systems, composed of particles characterized by local interaction potentials, independent of spins, whose properties are well described by the s-wave scattering length. There are several books [1-4] and review articles [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] covering different aspects of such bosonic systems with spin-independent local interaction potentials.In the present review, bosonic atoms or molecules are treated interacting through nonlocal interaction potentials, such as dipolar potential, and interacting through spinor forces that are local but depending on the effective spins related to hyperfine states. Although there exist reviews devoted to dipolar [20][21][22][23][24][25] and spinor [26,27] systems (see also [3,28]) the present paper differs from them in the following aspects. First, our aim here is not a brief enumeration of particular cases, numerical calculations, and different experiments, but the attention here is concentrated on the principal theoretical points allowing for the correct treatment of dipolar and spinor systems. Second, more attention is payed to the derivation of effective spin Hamiltonians for atoms and molecules in optical lattices. Third, the possibility of spintronics with cold atoms and molecules, interacting through dipolar and spinor forces, is discussed.The exposition of the material is organized so that the main mathematical points be clear to the reader. More technical details can be found in the tutorials [29,30]. Throughout the paper, the system of units is employed where the Boltzmann and Planck constants are set to one, k B = 1 and = 1.As is evident, the equation for the vacuum coherent field (2.40) differs form the equation (2.34) for the condensate function that is a coherent field, but, generally, not the vacuum coherent field. Equation (2.40) is a particular case of (2.34), where there are no uncondensed particles, so that ρ 1 , σ 1 , as well as ξ, are zero.One often confuses equation (2.40) for the vacuum coherent field with me...

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Transition states and thermal collapse of dipolar Bose-Einstein condensates

Cited by 9 publications

References 34 publications

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Normal form expansions and thermal decay rates of Bose-Einstein condensates with short- and long-range interaction

Dipolar and spinor bosonic systems

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