Quantum damping of Fermi-Pasta-Ulam revivals in ultracold Bose gases

Danshita, Ippei; Hipolito, Rafael; Oganesyan, Vadim; Polkovnikov, Anatoli

doi:10.1093/ptep/ptu041

Cited by 7 publications

(10 citation statements)

References 48 publications

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“…FPUT-like recurrences and SRs have also been observed and studied in other models. FPUT recurrences have been studied in the nonlinear Schrödinger equation, 21,22 interacting Bose gases, 23 and in the dynamics of anti-de Sitter space. 24 FPUT recurrences have been experiementally observed and studied in numerous systems including deep water-waves, 25 optical fibers, 26,27 spatial optics, 28 and magnetic films.…”

Section: Introductionmentioning

confidence: 99%

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences

Pace

Campbell

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We numerically investigate the existence and stability of higher-order recurrences (HoRs), including super-recurrences, supersuper-recurrences, etc., in the α and β Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two models breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the β-FPUT lattice is associated with the destruction of the so-called metastable state and thus with relaxation towards equilibrium. For the α-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable and far from equilibrium. We close with comments on the generality of our results for different lattice sizes.

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Section: Introductionmentioning

confidence: 99%

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences

Pace

Campbell

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…By numerically integrating the lattice model, T r was found to transition smoothly between β < 0 and β > 0 as a function of S. Interestingly, the maximum value of T r is located at S ∼ 4.2. Using the shifted-frequency perturbation theory, we extended results from reference [7] and found a closed form for T r , given in equation (19), which becomes a function of only S with an error of order O (N + 1) −2 . This expression was found to accurately describe T r for −12 S 4.…”

Section: Conclusion and Discussionmentioning

confidence: 86%

“…It can be seen that equation (19) is an accurate expression for the rescaled recurrence time in the domain −12 S 4. Writing equation (19) to first order in S yields…”

Section: Nearly Linear Regime Analyticsmentioning

confidence: 99%

“…We note that along with their central role in FPUT chains, FPUT recurrences have also been found and studied in numerous other theoretical models and also observed experimentally in various physical systems. Examples of the former include electron-phonon interactions [20], interacting Bose-Einstein condensates [19,21], ion waves [22], and anti-de Sitter spacetime [23,24]. The latter involves experimental demonstrations with electrical LC networks [25], plasmas [26], deep-water waves [27], silica optical fibers [28], magnetic film strips [29,30], and optics in a photorefractive crystal [31].…”

Section: Introductionmentioning

confidence: 99%

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The β Fermi-Pasta-Ulam-Tsingou recurrence problem

Pace

Reiss

Campbell

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We perform a thorough investigation of the first FPUT recurrence in the β-FPUT chain for both positive and negative β. We show numerically that the rescaled FPUT recurrence time Tr = tr/(N + 1) 3 depends, for large N , only on the parameter S ≡ Eβ(N + 1). Our numerics also reveal that for small |S|, Tr is linear in S with positive slope for both positive and negative β. For large |S|, Tr is proportional to |S| −1/2 for both positive and negative β but with different multiplicative constants. In the continuum limit, the β-FPUT chain approaches the modified Korteweg-de Vries (mKdV) equation, which we investigate numerically to better understand the FPUT recurrences on the lattice. In the continuum, the recurrence time closely follows the |S| −1/2 scaling and can be interpreted in terms of solitons, as in the case of the KdV equation for the α chain. The difference in the multiplicative factors between positive and negative β arises from soliton-kink interactions which exist only in the negative β case. We complement our numerical results with analytical considerations in the nearly linear regime (small |S|) and in the highly nonlinear regime (large |S|). For the former, we extend previous results using a shifted-frequency perturbation theory and find a closed form for Tr which depends only on S. In the latter regime, we show that Tr ∝ |S| −1/2 is predicted by the soliton theory in the continuum limit. We end by discussing the striking differences in the amount of energy mixing as well as the existence of the FPUT recurrences between positive and negative β and offer some remarks on the thermodynamic limit.

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“…This initial time, say t min , prior to which the pure state or eigenstate does not appear to be well approximated by a mixed thermal state is not very well understood or well reported quantity in the literature. Since ETH is still a relatively new field, only few studies have appeared which have considered the effects of finite N [45,46,47,48,49,50,51,52]. However one can try to make an estimate of this time.…”

Section: Finite N Effects: Early and Late Time Cut-offs On The Smearimentioning

confidence: 99%

Hologram of a pure state black hole

Roy

Sarkar

2015

Phys. Rev. D

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In this paper we extend the HKLL holographic smearing function method to reconstruct (quasi)local AdS bulk scalar observables in the background of a large AdS black hole formed by null shell collapse (a "pure state" black hole), from the dual CFT which is undergoing a sudden quench. In particular, we probe the near horizon and sub-horizon bulk locality. First we construct local bulk operators from the CFT in the leading semiclassical limit, N → ∞. Then we look at effects due to the finiteness of N , where we propose a suitable coarse-graining prescription involving early and late time cut-offs to define semiclassical bulk observables which are approximately local; their departure from locality being non-perturbatively small in N . Our results have important implications on the black hole information problem.

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Quantum damping of Fermi-Pasta-Ulam revivals in ultracold Bose gases

Cited by 7 publications

References 48 publications

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences

The β Fermi-Pasta-Ulam-Tsingou recurrence problem

Hologram of a pure state black hole

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