Hydrodynamics of local excitations after an interaction quench in 1<i>D</i>cold atomic gases

Franchini, Fabio; Kulkarni, Manas; Trombettoni, Andrea

doi:10.1088/1367-2630/18/11/115003

Cited by 14 publications

(12 citation statements)

References 102 publications

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“…In this model it has been conjectured that static dark solitons can be formed out of Lieb's type-II excitations [56,57] and numerical results seem to confirm this conjecture, although they are not yet conclusive about their dynamical stability [58][59][60][61]. In the context of quenches, the KdV and NLSE equations have been used for the study of dynamics of a soliton undergoing an interaction quench [32,40].…”

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confidence: 99%

Equilibration in one-dimensional quantum hydrodynamic systems

Sotiriadis¹

2017

J. Phys. A: Math. Theor.

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We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady state is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems. Contents

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confidence: 99%

Equilibration in one-dimensional quantum hydrodynamic systems

Sotiriadis¹

2017

J. Phys. A: Math. Theor.

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“…(1) which will change the nonlinearity coefficient (the coupling constant), κ → κ = κ/ √ η. Hence, it is feasible to realize this profile in the ultracold atom experiments by preparing a one-soliton state and subsequently quenching parameters of the holding trap and external fields to induce the change in the coupling constant [47][48][49][50].…”

Section: Attractive Interactionmentioning

confidence: 99%

Interplay of solitons and radiation in one-dimensional Bose gases

2019

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We study relaxation dynamics in one-dimensional Bose gases, formulated as an initial value problem for the classical nonlinear Schrödinger equation. We propose an analytic technique which takes into account the exact spectrum of nonlinear modes, that is both soliton excitations and dispersive continuum of radiation modes. Our method relies on the exact large-time asymptotics and uses the so-called dressing transformation to account for the solitons. The obtained results are quantitatively compared with the predictions of the linearized approach in the framework of the Bogoliubov theory. In the attractive regime, the interplay between solitons and radiation yields a damped oscillatory motion of the profile which resembles breathing. For the repulsive interaction, the solitons are confined in the sound cone region separated from the supersonic radiation. arXiv:1810.11409v4 [cond-mat.quant-gas]

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“…In this section we see the effects of suddenly changing a system parameter such as the coupling constant g. We mainly examine the changes in soliton evolution due to this quench [35,36]. In Fig.…”

Section: Quenchingmentioning

confidence: 99%

Duality in a hyperbolic interaction model integrable even in a strong confinement: multi-soliton solutions and field theory

Gon

Kulkarni

2019

J. Phys. A: Math. Theor.

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Models that remain integrable even in confining potentials are extremely rare and almost non-existent. Here, we consider a one-dimensional hyperbolic interaction model, which we call as the Hyperbolic Calogero (HC) model. This is classically integrable even in confining potentials (which have box-like shapes). We present a first-order formulation of the HC model in an external confining potential. Using the rich property of duality, we find multi-soliton solutions of this confined integrable model. Absence of solitons correspond to the equilibrium solution of the model. We demonstrate the dynamics of multi-soliton solutions via brute-force numerical simulations. We studied the physics of soliton collisions and quenches using numerical simulations. We have examined the motion of dual complex variables and found an analytic expression for the time period in a certain limit. We give the field theory description of this model and find the background solution (absence of solitons) analytically in the large-N limit. Analytical expressions of soliton solutions have been obtained in the absence of external confining potential. Our work is of importance to understand the general features of trapped interacting particles that remain classically integrable and can be of relevance to the collective behaviour of trapped cold atomic gases as well.

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Hydrodynamics of local excitations after an interaction quench in 1Dcold atomic gases

Cited by 14 publications

References 102 publications

Equilibration in one-dimensional quantum hydrodynamic systems

Equilibration in one-dimensional quantum hydrodynamic systems

Interplay of solitons and radiation in one-dimensional Bose gases

Duality in a hyperbolic interaction model integrable even in a strong confinement: multi-soliton solutions and field theory

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