Equilibration and approximate conservation laws: Dipole oscillations and perfect drag of ultracold atoms in a harmonic trap

Bamler, Robert; Rosch, Achim

doi:10.1103/physreva.91.063604

Cited by 10 publications

(9 citation statements)

References 39 publications

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“…Therefore, it is important to understand the properties of systems which are weakly perturbed away from integrability. 12,[44][45][46][47][48][49][50][51][52][53][54] In the case of classical mechanics, relevant formalism has been developed for more than fifty years, 55,56 whereas for quantum systems such understanding is still missing or, at least, remains largely incomplete. It is not evident to what extend the breaking of integrability may be described within a single universal picture and which properties are specific for particular model and/or perturbation.…”

Section: Introductionmentioning

confidence: 99%

Approximate conservation laws in perturbed integrable lattice models

2015

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We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying the algorithm to the perturbed XXZ model we find that the main effect of perturbation consists in expanding the support of conserved quantities. This expansion follows quadratic dependence on the strength of perturbation. The latter result together with correlation functions of conserved quantities obtained from the memory function analysis confirm feasibility of the perturbation theory.

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Section: Introductionmentioning

confidence: 99%

Approximate conservation laws in perturbed integrable lattice models

2015

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“…By combining Eqs. (26) and (27) we conclude that 1/τ ⊥ is finite if and only if there exists a wave-number q * such that ω 0→1 {2l} (q * ) < ω 0→0 (q * ). In fact since for n > 0,…”

Section: Relaxation Of Dos In Quasi-1d Systems At T =mentioning

confidence: 74%

Thermalization of dipole oscillations in confined systems by rare collisions

Khodas

Levchenko

2018

Phys. Rev. B

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We study the relaxation of the center-of-mass, or dipole oscillations in the system of interacting fermions confined spatially. With the confinement frequency ω ⊥ fixed the particles were considered to freely move along one (quasi-1D) or two (quasi-2D) spatial dimensions. We have focused on the regime of rare collisions, such that the inelastic collision rate, 1/τin ≪ ω ⊥ . The dipole oscillations relaxation rate, 1/τ ⊥ is obtained at three different levels: by direct perturbation theory, solving the integral Bethe-Salpeter equation and applying the memory function formalism. As long as anharmonicity is weak, 1/τ ⊥ ≪ 1/τin the three methods are shown to give identical results. In quasi-2D case 1/τ ⊥ = 0 at zero temperature. In quasi-1D system 1/τ ⊥ ∝ T 3 if the Fermi energy, EF lies below the critical value, EF < 3ω ⊥ /4. Otherwise, unless the system is close to integrability, the rate 1/τ ⊥ has the temperature dependence similar to that in quasi-2D. In all cases the relaxation results from the excitation of particle-hole pairs propagating along unconfined directions resulting in the relationship 1/τ ⊥ ∝ 1/τin, with the inelastic rate 1/τin = 0 as the phase-space opens up at finite energy of excitation, ω ⊥ . While 1/τ ⊥ ∝ τin in the hydrodynamic regime, ω ⊥ ≪ 1/τin, in the regime of rare collisions, ω ⊥ ≫ 1/τin, we obtain the opposite trend 1/τ ⊥ ∝ 1/τin.

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“…where E ± was defined in Eq. (9). Note that all the considerations up to this point have been exact.…”

Section: B Strong Socmentioning

confidence: 94%

Spin Hall mode in a trapped thermal Rashba gas

et al. 2017

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We theoretically investigate a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling and no interatomic interactions. In analogy with the spin Hall effect in uniform space, the gas exhibits a spin Hall mode. In particular, in response to a displacement of the center of mass of the system, spin-dipole moment oscillations occur. We determine the properties of these oscillations exactly and find that their amplitude strongly depends on the spin-orbit-coupling strength and the quantum statistics of the particles.

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Equilibration and approximate conservation laws: Dipole oscillations and perfect drag of ultracold atoms in a harmonic trap

Cited by 10 publications

References 39 publications

Approximate conservation laws in perturbed integrable lattice models

Approximate conservation laws in perturbed integrable lattice models

Thermalization of dipole oscillations in confined systems by rare collisions

Spin Hall mode in a trapped thermal Rashba gas

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