Energy Spectra of Vortex Distributions in Two-Dimensional Quantum Turbulence

Bradley, Ashton S.; Anderson, Brian P.

doi:10.1103/physrevx.2.041001

Cited by 132 publications

(238 citation statements)

References 73 publications

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“…There are many studies for 2D QT [129,130,138,139,140,141,142,143,144,145,146,147,148,149], some of which discuss the possibility of the inverse cascade in QT. To our understanding, the existence of the inverse cascade in QT is controversial.…”

Section: Inverse Cascade Of 2d Qtmentioning

confidence: 99%

Numerical Studies of Quantum Turbulence

2017

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We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose-Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross-Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed in revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose-Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates e.g. two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, etc., some of which has not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally we discuss open problems.

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Section: Inverse Cascade Of 2d Qtmentioning

confidence: 99%

Numerical Studies of Quantum Turbulence

2017

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“…These vortices have a characteristic core structure determined by the balance of kinetic energy and distortion energy, leading to a core size on the order of the healing length ξ [4,14]. Vortices with overlapping cores have complicated dynamics that couple the vortex gas to phonon excitations in the BEC and lead to the annihilation of vortex-antivortex pairs.…”

Section: Point Vortex Modelmentioning

confidence: 99%

“…The kinetic energy spectrum of N point vortices is determined by their spatial configuration and charges as derived by Novikov [12] and in more recent studies of BEC vortices with a characteristic vortex core structure [4]. For a given vortex configuration, the energy spectrum of N vortices in an unbounded plane is given as [12] …”

Section: Energy Spectrum and Vorticity Correlationmentioning

confidence: 99%

“…Clustering of vortices is also at the origin of an inverse energy cascade in driven QT [3,5,11], but in this case the mere existence of vortex * audun.skaugen@fys.uio.no clusters is not enough; their structure is crucially important and different from the equilibrium Onsager vortices emerging in decaying turbulence. Novikov [12] showed that, in principle, an inverse energy cascade with the Kolmogorov spectrum can be produced by a single cluster of same-sign vortices when there are long-range correlations in their spatial distribution such that the pair distribution function decays as a power law r −4/3 with the separation distance r. The dependence of the energy spectrum on the vortex configuration was further explored in this idealized case of same-sign point vortices [4,13]. However, any realistic model of driven QT needs to include both vortex signs, which complicates this idealized picture.…”

Section: Introductionmentioning

confidence: 99%

“…Quantum turbulence (QT) in highly oblate Bose Einstein condensates (BECs) provides a close experimental realization of 2D turbulence through the dynamics of quantized vortices and a well-defined theoretical framework to study turbulence from the statistical properties of a quantized vortex gas. In recent years, there have been indirect experimental evidence [2] and tantalizing numerical results [3][4][5] of the existence of an inverse energy cascade that follows the Kolmogorov scaling analogously to the classical turbulence. The condensation of energy on large scales has also been investigated in decaying quantum turbulence [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Origin of the inverse energy cascade in two-dimensional quantum turbulence

Skaugen

Angheluta

2017

Phys. Rev. E

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We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum k −5/3 on inertial scales r corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as r −4/3 . To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.

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Supersymmetric Hamiltonian and Vortex Formation Model in a Quantum Nonlinear System in an Inhomogeneous Electromagnetic Field

Manzetti

Trounev

2019

Advcd Theory and Sims

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Vortices and quasiparticles in 2D systems are studied for the last decades in relation to the development of technologies in quantum electromagnetics, optics, and quantum computation. Hamiltonians are a fundamental part for studying quasiparticles and vortices, and provide models to calculate the eigenvalues and eigenfunctions that describe a real physical state. By devising supersymmetry, a Hamiltonian for the description of vortices is developed forming in an 2D electron gas and study the numerical solutions under the effects of an alternating electromagnetic field. The numerical analysis shows that vorticity is formed spontaneously without symmetry-breaking and vortices arise from the boundaries and converge toward the center of the system in a similar fashion to natural hydrodynamic phenomena in water or plasma. Additionally, the equation under damping conditions is studied, a homogenous magnetic field and under the absence of an electromagnetic field. The results and the study of the parameters indicate that the supersymmetic wave equation (SWE) may be a good model equation to describe vorticity for quantum electromagnetics, hydrodynamics, and other physical phenomena in the realm of physical and quantum physical sciences. levels of n. The model is similar to the Laughlin model which describes the formation of quasiparticles in a quantum hall, [2] however it acts as an extension in describing vorticity and quantum rotation. These vortices are in essence Bose-Einstein condensates [3] which arise at ultra-low temperatures within a gas such as Helium, also known as superfluids or quantum fluids. This phenomenon gives rise to properties such as superfluidity and superconductivity in gases and metals, where a common quantum state arises for holes with the same vorticity, and hence lead to a uniform band for superconductivity and superfluidity. This phenomenon is of particular appeal to quantum computing and quantum optics. [4][5][6][7] Additionally, quantum computing and optical technologies can be developed further also by constructing systems with alternating magnetic fields, which provide an auxiliary effect on the vortices and generates quantum wave dynamics that trigger exotic properties of appeal to the scientific community. For instance, systems of particles subjected to impulse (staggered) magnetic fields have been studied in ultra-cold atoms recently. [8] The study shows that electronic band structures formed under the effects of the variable magnetic field affect the shape of the Dirac cones formed in the conduction band, hence leading to changes in conductivity. Interestingly, the same study shows that the effect of a staggered magnetic field on bosons generates superfluid phases [8] leading to zero viscosity and therefore zero resistance in the optical band. Furthermore, a second study, [9] shows that staggered electromagnetic fields lead to the formation of uniform superfluids and Mott insulating phases [10] and a novel kind of finite-momentum superfluid phase, directly tunable by the quantized stagg...

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Energy Spectra of Vortex Distributions in Two-Dimensional Quantum Turbulence

Cited by 132 publications

References 73 publications

Numerical Studies of Quantum Turbulence

Numerical Studies of Quantum Turbulence

Origin of the inverse energy cascade in two-dimensional quantum turbulence

Supersymmetric Hamiltonian and Vortex Formation Model in a Quantum Nonlinear System in an Inhomogeneous Electromagnetic Field

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