Numerical analysis of a self-similar turbulent flow in Bose–Einstein condensates

Семисалов, Б. В.; Grebenev, V. N.; Медведев, С. Б.; Nazarenko, Sergey

doi:10.1016/j.cnsns.2021.105903

Cited by 24 publications

(18 citation statements)

References 32 publications

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“…The WKE is solved numerically by adapting the method developed in [6] and by using a second order Runge-Kutta method for time marching. The integrals of the collision term are computed using decomposition of the domain of integration into bounded subdomains, inside of which the integrands are highly-smooth functions.…”

Section: B Wave-kinetic Equationmentioning

confidence: 99%

“…Such a method enables one to resolve possible singularities of spectra, and it is well suited for the collisional kernel of the GPE based WKE. The numerical method developed in [6] is highly accurate and efficient. More details can be found in Appendix B and in [6].…”

Section: B Wave-kinetic Equationmentioning

confidence: 99%

“…The numerical method developed in [6] is highly accurate and efficient. More details can be found in Appendix B and in [6].…”

Section: B Wave-kinetic Equationmentioning

confidence: 99%

“…Special attention in past literature was given to studies of stationary scaling solutions of this equation which are analogous to the Kolmogorov spectrum of hydrodynamic turbulence, the so-called Kolmogorov-Zakharov (KZ) spectra. However, nonstationary WT is also interesting because it is often characterized by mathematically nontrivial solutions exhibiting self-similar asymptotic [1][2][3][4][5][6]. Moreover, WWTT can be also extended to describing the higher-order moments and even to the full joint probability density function (PDF) of the wave intensities [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Testing wave turbulence theory for Gross-Pitaevskii system

Zhu,

Semisalov,

Krstulovic

et al. 2021

Preprint

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We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both, the waveaction spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of GP data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the breakdown of the theoretical assumptions underlying the WKE. Furthermore, we study how the wave statistics evolves toward Gaussianity in a time scale of the order of the kinetic time. The excellent agreement between direct numerical simulations of the GPE and the WKE provides a new and solid ground to the theory of weak wave turbulence.

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Section: B Wave-kinetic Equationmentioning

confidence: 99%

Section: B Wave-kinetic Equationmentioning

confidence: 99%

“…The numerical method developed in [6] is highly accurate and efficient. More details can be found in Appendix B and in [6].…”

Section: B Wave-kinetic Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Testing wave turbulence theory for Gross-Pitaevskii system

Zhu,

Semisalov,

Krstulovic

et al. 2021

Preprint

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“…Since then, much progress has been made in characterizing turbulent flows in BECs. The advances and state of the art concerning this topic can be found in Reference [26], for example. Here, we will discuss two references that capture the essential physical aspects of our experiment.…”

Section: Momentum Distributionsmentioning

confidence: 99%

Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

et al. 2021

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Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose–Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

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Feynman rules for forced wave turbulence

Rosenhaus

Smolkin

2023

J. High Energ. Phys.

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It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order.

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Numerical analysis of a self-similar turbulent flow in Bose–Einstein condensates

Cited by 24 publications

References 32 publications

Testing wave turbulence theory for Gross-Pitaevskii system

Testing wave turbulence theory for Gross-Pitaevskii system

Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

Feynman rules for forced wave turbulence

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