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We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de BroglieBohm quantum trajectories. The particle wave function can be modeled as a sum of two terms ψ = ψ_ (...
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We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de BroglieBohm quantum trajectories. The particle wave function can be modeled as a sum of two terms ψ = ψ_ (ingoing) + ψ_ (outgoing). A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of quantum vortices. The flow structure around each vortex displays a characteristic pattern called "nodal pointX point complex". The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal pointX point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the times of flight of particles following quantum trajectories from the source to detectors placed at various scattering angles θ, and thereby propose an experimental test of the de BroglieBohm formalism.
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The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and a...
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The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and an approximation for the density background is useful to understand vortex motion. We analyze the vortex motion on a variety of background configurations motivated by experiments on trapped Bose-Einstein condensates including linear and quadratic traps. We show that close to the center of the condensate cloud in the Thomas-Fermi regime the vortex is moving predominantly due to the image vortex that is effectively shifted because of the large density depletion of the condensate at the boundary. Close to the boundary the vortex moves mostly due to a large background density gradient across the vortex core. The vortex velocity is a nonlinear combination of these effects and of the global shape of the background density. We find the complete families of the traveling coherent structures in an infinitely long two-dimensional channel and derive an approximation of the velocity of a single vortex moving close to the center of the channel in the Thomas-Fermi regime.
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Quantum vortices were predicted to exist in superfluids 60 years ago by Onsager [1], with the superfluid circulation about the vortex core quantized in units of lc = h/m. They were subsequently found by Vinen [2] in superfluid 4He...
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Quantum vortices were predicted to exist in superfluids 60 years ago by Onsager [1], with the superfluid circulation about the vortex core quantized in units of lc = h/m. They were subsequently found by Vinen [2] in superfluid 4He. The ensuing developments form one of the great sagas of modern physics, in which major chapters include (i) the prediction of similar vortices in superconductors by Abrikosov [3], leading to a, vast experimental and technological enterprise; and (ii) the elucidation of very complex vortex structures in exotic superfluids like 3He [4] (and subsequently in various p-wave and d-wave superconductors, and in cold alkali Fermi gases), where the order parameter is much more complicated than in simple Bose superfluids or s-wave superconductors.
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We study the formation of topological defects (quantum vortices) during the formation of a two-dimensional (2D) polariton condensate at the Gamma point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies th...
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We study the formation of topological defects (quantum vortices) during the formation of a two-dimensional (2D) polariton condensate at the Gamma point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as 0.95 +/- 0.05. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We moreover demonstrate that the vortices can be pinned to the lattice, which prevents their recombination and could facilitate their observation and counting in continuous wave experiments.
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The term "quantum turbulence" (QT) unifies the wide class of phenomena where the chaotic set of one dimensional quantized vortex filaments (vortex tangles) appear in quantum fluids and greatly influence various physical features. ...
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The term "quantum turbulence" (QT) unifies the wide class of phenomena where the chaotic set of one dimensional quantized vortex filaments (vortex tangles) appear in quantum fluids and greatly influence various physical features. Quantum turbulence displays itself differently depending on the physical situation, and ranges from quasi-classical turbulence in flowing fluids to a near equilibrium set of loops in phase transition. The statistical configurations of the vortex tangles are certainly different in, say, the cases of counterflowing helium and a rotating bulk, but in all the physical situations very similar theoretical and numerical problems arise. Furthermore, quite similar situations appear in other fields of physics, where a chaotic set of one dimensional topological defects, such as cosmic strings, or linear defects in solids, or lines of darkness in nonlinear light fields, appear in the system. There is an interpenetration of ideas and methods between these scientific topics which are far apart in other respects. The main purpose of this review is to bring together some of the most commonly discussed results on quantum turbulence, focusing on analytic and numerical studies. We set out a series of results on the general theory of quantum turbulence which aim to describe the properties of the chaotic vortex configuration, starting from vortex dynamics. In addition we insert a series of particular questions which are important both for the whole theory and for the various applications. We complete the article with a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. We discuss this problem from the point of view of the theoretical results stated in the previous sections. We also included section, which is devoted to the experimental and numerical suggestions based on the discussed theoretical models.
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The nonstationary dynamics of vortices in conventional type II superconductors and in neutron stars is examined in the Newtonian approximation. A relaxation equation is obtained for vortices approaching an equilibrium distribution...
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The nonstationary dynamics of vortices in conventional type II superconductors and in neutron stars is examined in the Newtonian approximation. A relaxation equation is obtained for vortices approaching an equilibrium distribution after a change in an external magnetic field. The relaxation times are estimated for vortices in low-temperature superconductors and for proton vortices in the superconducting core of a neutron star. It is shown that the proton vortex system created by entrainment currents is rigidly coupled to the neutron vortices.
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We study the dynamics of a rotating trapped Bose-Einstein condensate (BEC) at finite temperatures. Using the Zaremba-Nikuni-Griffin formalism, based on a generalized Gross-Pitaevskii equation for the condensate coupled to a semicl...
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We study the dynamics of a rotating trapped Bose-Einstein condensate (BEC) at finite temperatures. Using the Zaremba-Nikuni-Griffin formalism, based on a generalized Gross-Pitaevskii equation for the condensate coupled to a semiclassical kinetic equation for a thermal cloud, we numerically simulate vortex lattice formation in the presence of a time-dependent rotating trap potential. At low rotation frequency, the thermal cloud undergoes rigid body rotation, while the condensate exhibits irrotational flow. Above a certain threshold rotation frequency, vortices penetrate into the condensate and form a vortex lattice. Our simulation result clearly indicates a crucial role for the thermal cloud, which triggers vortex lattice formation in the rotating BEC.
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A review of various exactly solvable models on the determination of the energy spectra E(k) of 3D-velocity field, induced by chaotic vortex lines is proposed. This problem is closely related to the sacramental question whether a c...
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A review of various exactly solvable models on the determination of the energy spectra E(k) of 3D-velocity field, induced by chaotic vortex lines is proposed. This problem is closely related to the sacramental question whether a chaotic set of vortex filaments can mimic the real hydrodynamic turbulence. The quantity can be exactly calculated, provided that we know the probability distribution functional P({s(ξ,t)}) of vortex loops configurations. The knowledge of P({s(ξ, t)}) is identical to the full solution of the problem of quantum turbulence and, in general, P is unknown. In the paper we discuss several models allowing to evaluate spectra in the explicit form. This cases include standard vortex configurations such as a straight line, vortex array and ring. Independent chaotic loops of various fractal dimension as well as interacting loops in the thermodynamic equilibrium also permit an analytical solution. We also describe the method of an obtaining the 3D velocity spectrum induced by the straight line perturbed with chaotic 1D Kelvin waves on it.
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The problem of the statistics of a set of chaotic vortex lines in counterflowing superfluid helium is studied. We introduced a Langevin-type force into the equation of motion of the vortex line in the presence of relative velocity...
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The problem of the statistics of a set of chaotic vortex lines in counterflowing superfluid helium is studied. We introduced a Langevin-type force into the equation of motion of the vortex line in the presence of relative velocity . This random force is supposed to be Gaussian satisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planck equation for probability functional in the vortex loop configuration space is shown to have a solution in the form of Gibbs distribution with the substitution , where is the energy of the vortex configuration and is the Lamb impulse. Some physical consequences of this fact are discussed.
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We numerically study two-dimensional quantum turbulence by using the Gross-Pitaevskii model and the Vortex-Point model. Two-dimensional classical turbulence has long been investigated as an ideal system of geophysical phenomena. T...
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We numerically study two-dimensional quantum turbulence by using the Gross-Pitaevskii model and the Vortex-Point model. Two-dimensional classical turbulence has long been investigated as an ideal system of geophysical phenomena. The amazing character of this turbulence is inverse energy cascade which carries energy toward low wavenumbers and excites large-scale motion. We expect these phenomena in two-dimensional quantum turbulence because in three-dimensional turbulence we know classical and quantum analogue. However, we have not yet confirmed inverse cascade in two-dimensional quantum turbulence. In this work, we show numerical results and discuss why inverse cascade does not occur in two-dimensional quantum turbulence by referring to the mechanism of two-dimensional classical turbulence.
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