Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

Kati, Yagmur; Yu, Xiaoquan; Flach, Sergej

doi:10.21468/scipostphyscore.3.2.006

Cited by 9 publications

(5 citation statements)

References 29 publications

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“…The BdG equations are particle-hole symmetric [λ ν , {χ ν , Π ν }] ←→ [−λ ν , {Π ν , χ ν }] (ν is the mode number). This yields the solution χ = Π ∝ G l for λ ν = 0 as follows also readily from inspecting (24), independently of the choice of the GS field. The eigenvector to λ = 0 can be also obtained from the observation that δ is time-independent by Eq.…”

Section: Elementary Excitationsmentioning

confidence: 67%

“…By fixing the norm density, we numerically minimize the energy by varying the real and nonnegative variables G for a given disorder realization as in Ref. [24] (see also Appendix A). The resulting ground-state density distribution G 2 is plotted in Fig.…”

Section: Ground State Propertiesmentioning

confidence: 99%

“…Disorder introduces an additional energy scale W . It induces long-time relaxation dynamics and glass phases, the Anderson localization [20], and the Lifshits "glass" phase [21][22][23][24][25], to name a few. The presence of interactions strongly influences Anderson localization (see, e.g., the reviews [26][27][28]).…”

Section: Introductionmentioning

confidence: 99%

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Anderson localization of excitations in disordered Gross-Pitaevskii lattices

Kati,

Fistul,

Cherny

et al. 2021

Preprint

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We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the weak and strong interaction regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov-de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For strong interactions, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective strong interaction field equations for the excitations and generalize to higher dimensions.

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Section: Elementary Excitationsmentioning

confidence: 67%

Section: Ground State Propertiesmentioning

confidence: 99%

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Anderson localization of excitations in disordered Gross-Pitaevskii lattices

Kati,

Fistul,

Cherny

et al. 2021

Preprint

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“…In Refs. [22,23,24,25,26,28,29,30,31,32,33,34] it was shown that Anderson localization is destroyed by the presence of nonlinearity, resulting to the subdiffusive spreading of energy due to deterministic chaos. Such results rely on the accurate, long time integration of the systems' equations of motion and variational equations.…”

Section: Introductionmentioning

confidence: 99%

Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions

Danieli¹,

Manda²,

Mithun³

et al. 2019

Mathematics in Engineering

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We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the Fermi-Pasta-Ulam-Tsingou (FPUT) chain and the one-and two-dimensional disordered, discrete nonlinear Schrödinger equations (DDNLS). In our analysis we consider methods based on Taylor series expansion, Runge-Kutta discretization and symplectic transformations. The latter have the ability to exactly preserve the symplectic structure of Hamiltonian systems, which results in keeping bounded the error of the system's computed total energy. We perform extensive numerical simulations for several initial conditions of the studied models and compare the numerical efficiency of the used integrators by testing their ability to accurately reproduce characteristics of the systems' dynamics and quantify their chaoticity through the computation of the maximum Lyapunov exponent. We also report the expressions of the implemented symplectic schemes and provide the explicit forms of the used differential operators. Among the tested numerical schemes the symplectic integrators ABA864 and S RKN a 14 exhibit the best performance, respectively for moderate and high accuracy levels in the case of the FPUT chain, while for the DDNLS models s9ABC6 and s11ABC6 (moderate accuracy), along with s17ABC8 and s19ABC8 (high accuracy) proved to be the most efficient schemes.are the 2N × 2N elements of the Hessian matrix D 2 H (x(t)) of the Hamiltonian function H computed on the phase space trajectory x(t). Eq. (3.5) is linear in w(t), with coefficients depending on the system's trajectory x(t). Therefore, one has to integrate the variational equations (3.5) along with the equations of motion (3.2), which means to evolve in time the general vector X(t) = (x(t), δx(t)) by solving the systemẊH (x(t)) · δx(t).( 3.7) In what follows we will briefly describe several numerical schemes for integrating the set of equations (3.7).

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“…Treating infinite particle numbers with mean-field approximations results in nonlinear add-ons to the wave dynamics which stem from the two-body interactions. Nonlinear wave packet expansion was investigated both analytically and numerically over vast time scales [26][27][28][29][30][31]. It allows to obtain the details of the subdiffusion process, with expansion times which are many orders of magnitude larger than comparable experimental simulations [32].…”

mentioning

confidence: 99%

Logarithmic expansion of many-body wave packets in random potentials

Mallick,

Flach

2021

Preprint

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Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length ξ. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, ii) an interaction strength ramping to speed up the subdiffusion, and iii) an action quantization of the nonlinear terms. We observe the saturation of the cloud expansion of N particles to a volume ∼ N ξ. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean field diffusion with the final quantum saturation regime and is entirely controlled by particle number N . The temporal window of that regime grows exponentially with the localization length ξ.

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Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

Cited by 9 publications

References 29 publications

Anderson localization of excitations in disordered Gross-Pitaevskii lattices

Anderson localization of excitations in disordered Gross-Pitaevskii lattices

Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions

Logarithmic expansion of many-body wave packets in random potentials

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