Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions

El, Gennady; Камчатнов, А. М.; Pavlov, Maxim V.; Zykov, S. A.

doi:10.1007/s00332-010-9080-z

Cited by 72 publications

(162 citation statements)

References 51 publications

(192 reference statements)

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“…the observation of interesting "soliton molecules" [22]. The ability to generate large numbers of dark-bright solitons with well defined initial periodicity may also be an effective starting point for investigations of soliton gases [23,24].…”

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Phase Winding a Two-Component Bose-Einstein Condensate in an Elongated Trap: Experimental Observation of Moving Magnetic Orders and Dark-Bright Solitons

et al. 2013

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We experimentally investigate the phase winding dynamics of a harmonically trapped twocomponent BEC subject to microwave induced Rabi oscillations between two pseudospin components. While the single-particle dynamics can be explained by mapping the system to a twocomponent Bose-Hubbard model, nonlinearities due to the interatomic repulsion lead to new effects observed in the experiments: In the presence of a linear magnetic field gradient, a qualitatively stable moving magnetic order that is similar to antiferromagnetic order is observed after critical winding is achieved. We also demonstrate how the phase winding can be used to generate copious dark-bright solitons in a two-component BEC, opening the door for new experimental studies of these nonlinear features.PACS numbers: 03.75. Kk, 03.75.Mn, 03.75.Lm, 05.45.Yv Ferromagnetic and antiferromagnetic (AF) orders are two important and fundamental linear magnetic orders in material physics. For instance, it is well known that AF order exists in the underdoped and low temperature region of the phase diagram for high temperature cuprate superconductors [1]. Ultra-cold atoms provide a clear and highly controllable experimental platform for emulating various condensed matter phenomena. In ultracold atomic gases, AF order has been predicted to exist for both bosons and fermions confined in optical lattices, but reaching the required low temperatures is very difficult [2,3]. For cold atoms confined in optical lattices, AF order corresponds to a quantum state where atoms at alternating lattice sites have opposite pseudospins and possess long range phase coherence. For a continuous two-component BEC in a harmonic trap, there are no such discrete lattice sites, but an AF order can still be defined similarly to that in lattices. Each spin component contains periodic and spatially well separated parts and different spin components appear alternating in space. In lattice system, the lattice periodicity sets the AF length scale, whence for a continuous system the minimum domain spacing is limited by the spin healing length. Twocomponent BECs contain rich physics and have been investigated extensively in the past decade in both experiment and theory [4]. Notable phenomena include the analogy to Josephson junction effects for a BEC in a double well potential [5,6], the interaction induced phase separation [7,8], counterflow induced modulational instability [9], novel types of solitons [9], etc.In this Letter, we experimentally investigate the dynamics of an elongated two-component BEC subject to a Rabi coupling between the two components exposed in the presence of a linear magnetic field gradient. We show that the dynamics can lead to a phase resembling AF order. The strong nonlinear interactions in the BEC play a key role, without them periodic winding/unwinding cycles analogous to the ones of [10,11] model that explains these regular cycles. For the nonlinear case, our experiment and numerics show a succession of stages during the winding. First a period of regular winding...

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Phase Winding a Two-Component Bose-Einstein Condensate in an Elongated Trap: Experimental Observation of Moving Magnetic Orders and Dark-Bright Solitons

et al. 2013

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“…System (2.6) was studied in [8] in the investigation of the so-called multiflow cold gas reductions of the nonlocal kinetic equation derived as the thermodynamical limit of the averaged multi-phase solutions of the KdV equation by the Whitham method.…”

Section: Linearly Degenerate Solutions To the Wdvv Associativity Equamentioning

confidence: 99%

Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations

Dubrovin

Pavlov

Zykov

2011

Funct Anal Its Appl

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Abstract. We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.

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“…The isospectral cold-gas reductions (5), (6) were proven in [2] to represent integrable (semi-Hamiltonian [9]) linearly degenerate hydrodynamic type systems (see [5], [7]) for arbitrary N , which is a strong indication that the full kinetic equation (1), (2) could constitute an integrable system in the sense yet to be explored.…”

Section: Introductionmentioning

confidence: 99%

“…In recent paper [2], the multi-flow hydrodynamic reductions of the kinetic equation (1), (2) were studied using the so-called 'cold-gas' ansatz…”

Section: Introductionmentioning

confidence: 99%

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Generalized hydrodynamic reductions of the kinetic equation for a soliton gas

Pavlov

Taranov

2012

Theor Math Phys

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Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions

Cited by 72 publications

References 51 publications

Phase Winding a Two-Component Bose-Einstein Condensate in an Elongated Trap: Experimental Observation of Moving Magnetic Orders and Dark-Bright Solitons

Phase Winding a Two-Component Bose-Einstein Condensate in an Elongated Trap: Experimental Observation of Moving Magnetic Orders and Dark-Bright Solitons

Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations

Generalized hydrodynamic reductions of the kinetic equation for a soliton gas

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