Vortex Density Research Articles

Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap.

We consider vortex dynamics in the context of Bose-Einstein condensates (BECs) with a rotating trap, with or without anisotropy. Starting with the Gross-Pitaevskii (GP) partial differential equation (PDE), we derive a novel reduced system of ordinary differential equations (ODEs) that describes stable configurations of multiple co-rotating vortices (vortex crystals). This description is found to be quite accurate quantitatively especially in the case of multiple vortices. In the limit of many vortices, BECs are known to form vortex crystal structures, whereby vortices tend to arrange themselves in a hexagonal-like spatial configuration. Using our asymptotic reduction, we derive the effective vortex crystal density and its radius. We also obtain an asymptotic estimate for the maximum number of vortices as a function of rotation rate. We extend considerations to the anisotropic trap case, confirming that a pair of vortices lying on the long (short) axis is linearly stable (unstable), corroborating the ODE reduction results with full PDE simulations. We then further investigate the many-vortex limit in the case of strong anisotropic potential. In this limit, the vortices tend to align themselves along the long axis, and we compute the effective one-dimensional vortex density, as well as the maximum admissible number of vortices. Detailed numerical simulations of the GP equation are used to confirm our analytical predictions.

Dynamics of a quantum phase transition in the Bose-Hubbard model: Kibble-Zurek mechanism and beyond

In this paper, we study the dynamics of the Bose-Hubbard model by using time-dependent Gutzwiller methods. In particular, we vary the parameters in the Hamiltonian as a function of time, and investigate the temporal behavior of the system from the Mott insulator to the superfluid (SF) crossing a second-order phase transition. We first solve a time-dependent Schr\"odinger equation for the experimental setup recently done by Braun et.al. [Proc. Nat. Acad. Sci. 112, 3641 (2015)] and show that the numerical and experimental results are in fairly good agreement. However, these results disagree with the Kibble-Zurek scaling. From our numerical study, we reveal a possible source of the discrepancy. Next, we calculate the critical exponents of the correlation length and vortex density in addition to the SF order parameter for a Kibble-Zurek protocol. We show that beside the "freeze" time $\hat{t}$, there exists another important time, $t_{\rm eq}$, at which an oscillating behavior of the SF amplitude starts. From calculations of the exponents of the correlation length and vortex density with respect to a quench time $\tQ$, we obtain a physical picture of a coarsening process. Finally, we study how the system evolves after the quench. We give a global picture of dynamics of the Bose-Hubbard model.

Direct numerical simulation of surfactant solution flow in the wide‐rib rectangular grooved channel

The turbulent flow of surfactant solution in the wide‐rib rectangular grooved channels was studied by direct numerical simulation. Moreover, the variations of near‐wall streamwise vortices with time were discussed and the distributions of streamwise vortex radius, swirling strength and density were quantitatively investigated. It was found that the influence of microgrooves on the fluid mainly occurred within the buffer layer and microgrooves could induce numerous streamwise vortices with small size and swirling strength within the grooved valleys. The drag‐reducing enhancement mechanism of microgroove in the surfactant solution could be mainly considered as the competing results between the “restriction effect” and “tip effect” of microgroove, and the essential factor should be the numerous secondary streamwise vortices with small size and swirling strength within the grooved valleys. Furthermore, a predicted method for the optimal drag‐reducing size of microgroove was proposed, and the prediction values agreed well with the numerical results. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2898–2912, 2018

Polarizability of electrically induced magnetic vortex “atoms”

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, draws a great attention, which has led to experimental success in creation and manipulation of single magnetic defects, such as skyrmions and domain walls. In this work we explore a scenario of electric field creation of another type of topological defects – magnetic vortices and antivortices. Because of interaction of magnetic and electric subsystems each magnetic vortex (antivortex) in magnetoelectric materials possesses quantized magnetic charge, responsible for interaction between vortices, and electric charge that couples them to electric field. This property of magnetic vortices makes possible their creation by electric fields. We show that the electric field, created by a cantilever tip, produces a “magnetic atom” with a localized spot of ordered vortices (“nucleus” of the atom) surrounded by antivortices (“electronic shells”). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically by Monte Carlo simulation.

Surface Effects on the Dynamic Behavior of Vortices in Type II Superconducting Strips with Periodic and Conformal Pinning Arrays

Using molecular dynamics techniques, we simulate the vortex behavior in a type II superconducting strip in the presence of triangular and two types of conformal pinning arrays, one with a pinning gradient perpendicular to the driving force (C1) and the other parallel (C2), at zero temperature. A transport force is applied in the infinite direction of the strip, and the magnetic field is increased until the rate between the density of vortices (n v ) and pinning (n p ) reaches n v /n p = 1.5. Our results show a monotonic increase, by steps, of the vortex density with the applied magnetic field. Besides, each pinning lattice presents a different vortex penetration delay. For the triangular pinning array, different than the case of infinite films, here the system exhibits only one pronounced depinning force peak at n v /n p = 1. However, the depinning force peak is present for only one value of field, in the range of fields where n v /n p = 1 is stable. For the case of conformal pinning arrays, in analogy to what is observed in infinite films, no commensurability depinning force peaks were found. In the present case, the C1 array is more efficient at low fields, all arrays are equivalent in the intermediate fields, and the C2 array is more efficient for high fields. We also show that for the C1 array at high fields, vortices depin following the conformal arches, from the edge to the center. For the C2 array, the depinning force is higher when compared to that of C1, because this particular conformal structure prevents the formation of easy vortex flow channels.

Tunneling decay of false vortices with gravitation

We study the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in three spacetime dimensions with gravity. The scenario considered is one in which the initial state, rather than being the homogeneous false vacuum, contains false vortices. The question addressed is whether, and, if so, under which circumstances, the presence of vortices has a significant catalyzing effect on vacuum decay. After studying the existence and properties of vortices, we study their decay rate through quantum tunneling using a variety of techniques. In particular, for so-called thin-wall vortices we devise a one-parameter family of configurations allowing a quantum-mechanical calculation of tunneling. Also for thin-wall vortices, we employ the Israel junction conditions between the interior and exterior spacetimes. Matching these two spacetimes reveals a decay channel which results in an unstable, expanding vortex. We find that the tunneling exponent for vortices, which is the dominant factor in the decay rate, is half that for Coleman-de Luccia bubbles. This implies that vortices are short-lived, making them cosmologically significant even for low vortex densities. In the limit of the vanishing gravitational constant we smoothly recover our earlier results for the decay of the false vortex in a model without gravity.

Emergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions.

We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Euler's equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement with numerical simulations of the point-vortex model.

Conformal Vortex Crystals

We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical simulations, we demonstrate that, for suitable choices of the force field, and bellow a certain transition temperature, the vortex system self-organizes into highly inhomogeneous conformal crystals in a way as to minimize the total energy. These nonuniform structures are topologically ordered and can be mathematically mapped into a triangular Abrikosov lattice via a conformal transformation. Above the crystallization temperature, the conformal vortex crystal becomes unstable and gives place to a nonuniform polycrystalline structure. We propose a simple method to engineer the potential energy profile necessary for the observation of conformal crystals of vortices, which can also be applied to other 2D particle systems, and suggest possible experiments in which conformal or quasi-conformal vortex crystals could be observed in bulk superconductors and in thin films.

Interaction of vortex ring with a stratified finite thickness interface

This work experimentally investigates the dynamics of interaction between a propagating vortex ring and density stratified interface of finite thickness. The flow evolution has been quantified using a high speed shadowgraph technique and particle image velocimetry. The spatial and temporal behaviours of the vortex in the near and far field of the interface and the plume structure formed due to buoyancy are investigated systematically by varying the vortex strength (Reynolds number, Re) and the degree of stratification (Atwood number, At). Maximum penetration length (Lpmax) of the vortex ring through the interface is measured over a range of Reynolds (1350 ≤ Re ≤ 4600) and Richardson (0.1 ≤ Ri ≤ 4) numbers. It is found that for low Froude number values, the maximum penetration length varies linearly with the Froude number as in the study of Orlandi et al. [“Vortex rings descending in a stratified fluid,” Phys. Fluids 10, 2819–2827 (1998)]. However, for high Reynolds and Richardson numbers (Ri), anomalous behaviour in maximum penetration is observed. The Lpmax value is used to characterize the vortex-interface interactions into non-penetrative, partially-penetrative, and extensively penetrative regimes. Flow visualization revealed the occurrence of short-wavelength instability of a plume structure, particularly in a partially penetrative regime. Fluid motion exhibits chaotic behaviour in an extensively penetrative regime. Detailed analyses of plume structure propagation are performed by measuring the plume length and plume rise. Appropriate scaling for the plume length and plume rise is derived, which allows universal collapse of the data for different flow conditions. Some information concerning the instability of the plume structure and decay of the vortex ring is obtained using proper orthogonal decomposition.

Phase transitions and vortex structure evolution in two-level high-temperature granular superconductor YBa2Cu3O7 – δ under temperature and magnetic field

Temperature dependences of the resistivity ρ(T) of samples of granular high-temperature superconductor YBa2Cu3O7 – δ are measured at various transverse external magnetic fields at 0 < H ext < 1900 Оe in the temperature range from the upper Josephson critical temperature of “weak bonds” T c2J to temperatures slightly exceeding the superconducting transition temperature T c . Based on the data obtained, the behavior of the field dependences of the critical temperatures of superconducting grains and “weak bonds,” and temperature and field dependences of the magnetic contribution to the resistivity \(\left[ {\Delta \rho \left( {T,H} \right) = \rho {{\left( T \right)}_{{H_{ext}} = const}} - \rho {{\left( T \right)}_{{H_{ext}} = 0}}} \right]\). It is shown that the behavior of the magnetic contribution to the resistivity Δρ along the line of the phase transition related to the onset of the magnetic field penetration in the form of Abrikosov vortices into the subsystem of superconducting grains T c1g (H ext) is anomalous. The concepts on the magnetic flux redistribution between both subsystems of two-level HTSC near in the vicinity of T c1g : the Josephson vortex decreases, and the Abrikosov vortex density increases.

Negative velocity fluctuations and non-equilibrium fluctuation relation for a driven high critical current vortex state

Under the influence of a constant drive the moving vortex state in 2H-NbS2 superconductor exhibits a negative differential resistance (NDR) transition from a steady flow to an immobile state. This state possesses a high depinning current threshold ({{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}) with unconventional depinning characteristics. At currents well above {{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}, the moving vortex state exhibits a multimodal velocity distribution which is characteristic of vortex flow instabilities in the NDR regime. However at lower currents which are just above {{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}, the velocity distribution is non-Gaussian with a tail extending to significant negative velocity values. These unusual negative velocity events correspond to vortices drifting opposite to the driving force direction. We show that this distribution obeys the Gallavotti-Cohen Non-Equilibrium Fluctuation Relation (GC-NEFR). Just above {{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}, we also find a high vortex density fluctuating driven state not obeying the conventional GC-NEFR. The GC-NEFR analysis provides a measure of an effective energy scale (Eeff) associated with the driven vortex state. The Eeff corresponds to the average energy dissipated by the fluctuating vortex state above {{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}. We propose the high Eeff value corresponds to the onset of high energy dynamic instabilities in this driven vortex state just above {{boldsymbol{I}}}_{{boldsymbol{c}}}^{{boldsymbol{h}}}.

Oriented ordering near line defects in crystals

General properties of directed ordering near line defects, in particular an edge dislocation, in elastic crystals undergoing phase transition are studied using the two-component time-dependent Ginzburg–Landau equation in two dimensions or 2D-XY model. The associated Landau potential comprises a sixth-order term, cubic anisotropy terms and the field of the dislocation. In thermodynamic equilibrium, the phase diagram for the model is delineated. Upon quenching the system below its transition point, the temporal evolution of the order parameter components in the vicinity of the defect is numerically evaluated. The development of vortices, emanated from the model, is explored and their interaction with the dislocation is examined. The dislocation produced a vortex free circular region whose diameter grew almost linearly with time. The time-dependence of vortex density for various settings of the Landau potential coefficients are evaluated. The vortex density (in 2D) decreased inversely with time, albeit faster in the absence of dislocation. By computing the two-point correlation function, we established that the dynamic scaling law is satisfied for the considered model if the distance is scaled by or by its half-width for a dislocation free crystal. Finally, phase transitions in improper ferroelectrics in the context of the model are discussed.

Polarizability of electrically induced magnetic vortex plasma

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, draws a great attention in recent years, which has led to experimental success in creation and manipulation by electric field of single magnetic defects, such as domain walls and skyrmions. In this work we explore a scenario of electric field creation of another type of topological defects -- magnetic vortices and antivortices, which are characteristic for materials with easy plane (XY) symmetry. Each magnetic (anti)vortex in magnetoelectric materials (such as type-II multiferroics) possesses a quantized magnetic and an electric charge, where the former is responsible for interaction between vortices and the latter couples the vortices to electric field. This property of magnetic vortices opens a peculiar possibility of creation of magnetic vortex plasma by non-uniform electric fields. We show that the electric field, created by a cantilever tip, produces a "magnetic atom" with a localized spatially ordered spot of vortices ("nucleus" of the atom) surrounded by antivortices ("electronic shells"). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically. We show that electric polarizability of the "magnetic atom" depends on temperature as $\alpha \sim 1/T^{1-\eta}$ ($\eta>0$), which is consistent with Euclidean random matrix theory prediction.

Core structure of two-dimensional Fermi gas vortices in the BEC-BCS crossover region

We report $T=0$ diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. We investigate how vortex core structure properties behave over the BEC-BCS crossover. We calculate the vortex excitation energy, density profiles, and vortex core properties related to the current. We find a density suppression at the vortex core on the BCS side of the crossover, and a depleted core on the BEC limit. Size-effect dependencies in the disk geometry were carefully studied.

On flame height of circulation-controlled firewhirls with variable physical properties and in power-law vortices: A mass-diffusivity-ratio model correction

This paper presents a theory on the flame height of circulation-controlled firewhirls, approximately combining variable physical properties, a power-law vortex model, and a mass-diffusivity-ratio model. The theoretical results show that the dimensionless flame height can be expressed as a multiplication of four dimensionless factors. The first factor is the stoichiometric-mixture-fraction-scaled Peclet number that was first identified by Chuah et al. (2011) in their theory based on the assumptions of Burgers vortex and constant physical properties. The second factor characterizes the axial flame-stretching effect found by Klimenko and Williams (2013) in their theory based on the assumptions of power-law strong vortex and constant physical properties. The third factor quantifies the effect of variable density, which was recently unveiled in Yu and Zhang's (2017) theory. The last factor describes the effect of distinct mass diffusivities of fuel and oxidizer, which has not been considered in the previous studies. Although integrating the first three factors in the theory would lead to an over-prediction to the flame height, accounting for the distinct mass diffusivities of fuel and oxidizer, leading to a mass-diffusivity-ratio model correction, results in the finding of a “reduction” mechanism for the flame height, which is comparable in order of magnitude with the other “enhancement” mechanisms obtained from considering either the power-law strong vortex or variable density.

Strain-induced intervortex interaction and vortex lattices in tetragonal superconductors

In superconductors with strong coupling between superconductivity and elasticity manifested in a strong dependence of transition temperature on pressure, there is an additional contribution to inter-vortex interactions due to the strain field generated by vortices. When vortex lines are along the $c$ axis of a tetragonal crystal, a square vortex lattice (VL) is favored at low vortex densities, because the vortex-induced strains contribution to the inter-vortex interactions is long range. At intermediate magnetic fields, the triangular lattice is stabilized. The triangular lattice evolves to the square lattice upon increasing magnetic field, and eventually the system locks to the square structure. We argue, however, that as $B$ approaches $H_{c2}$ the elastic inter-vortex interactions disappear faster than the standard London interactions, so that VL should return to the triangular structure. Our results are compared to VLs observed in the heavy fermion superconductor $\mathrm{CeCoIn_5}$.

Space-Time Vortex Driven Crossover and Vortex Turbulence Phase Transition in One-Dimensional Driven Open Condensates.

We find a first-order transition driven by the strength of nonequilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable nonequilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly nonthermal behavior. Below the transition, we identify a new time scale associated with noise-activated unbound space-time vortices, beyond which, the temporal coherence function changes from a Kardar-Parisi-Zhang-type subexponential to a disordered exponential decay. Experimental realization of the nonequilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.

Conductivity Contrast and Tunneling Charge Transport in the Vortexlike Ferroelectric Domain Patterns of Multiferroic Hexagonal YMnO3

We deduce the intrinsic conductivity properties of the ferroelectric domain walls around the topologically protected domain vortex cores in multiferroic YMnO_{3}. This is achieved by performing a careful equivalent-circuit analysis of dielectric spectra measured in single-crystalline samples with different vortex densities. The conductivity contrast between the bulk domains and the less conducting domain boundaries is revealed to reach up to a factor of 500 at room temperature, depending on the sample preparation. Tunneling of localized defect charge carriers is the dominant charge-transport process in the domain walls that are depleted of mobile charge carriers. This work demonstrates that, via equivalent-circuit analysis, dielectric spectroscopy can provide valuable information on the intrinsic charge-transport properties of ferroelectric domain walls, which is of high relevance for the design of new domain-wall-based microelectronic devices.

Bosonic analogs of the fractional quantum Hall state in the vicinity of Mott states

In this paper, the Bose-Hubbard model (BHM) with the nearest-neighbor (NN) repulsions is studied from the viewpoint of possible bosonic analogs of the fractional quantum Hall (FQH) state in the vicinity of the Mott insulator (MI). First, by means of the Gutzwiller approximation, we obtain the phase diagram of the BHM in a magnetic field. Then, we introduce an effective Hamiltonian describing excess particles on a MI and calculate the vortex density, momentum distribution, and the energy gap. These calculations indicate that the vortex solid forms for small NN repulsions, but a homogeneous featureless ``Bose metal'' takes the place of it as the NN repulsion increases. We consider particular filling factors at which the bosonic FQH state is expected to form. Chern-Simons (CS) gauge theory to the excess particle is introduced, and a modified Gutzwiller wave function, which describes bosons with attached flux quanta, is introduced. The energy of the excess particles in the bosonic FQH state is calculated using that wave function, and it is compared with the energy of the vortex solid and Bose metal. We found that the energy of the bosonic FQH state is lower than that of the Bose metal and comparable with the vortex solid. Finally, we clarify the condition that the composite fermion appears by using CS theory on the lattice that we previously proposed for studying the electron FQH effect.

Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

We demonstrate that in a wide range of heat fluxes the dynamics of heat transfer in superfluid helium is determined by the existence of remanent quantized vortices. The vortex density dynamics determines the rise of temperature near the heater and the boiling-up of superfluid helium. It permits to understand the results of the experiments of several groups.