Related papers: Quantized Vortex Dynamics of the Nonlinear Wave Eq…
Quantum vorticity in polariton systems has been traditionally investigated within the frame of many-body phenomena under the mean-field or coherent approaches. In the present work, we show that the fully quantized picture describes richer…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in…
Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states a torus with minor radius a and major radius R can…
Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry.…
We analyze the disorder limited motion of quantum vortices in a two-dimensional bosonic superfluid with a large healing length. It is shown that the excitations of low-energy degrees of freedom associated with the non-analytic…
We consider the damped/driver (modified) cubic NLS equation on a large torus with a properly scaled forcing and dissipation, and decompose its solutions to formal series in the amplitude. We study the second order truncation of this series…
We present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons,…
In this article, we review the research on the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. First, after briefly reviewing the earlier research and describing the current problems on quantized…
We consider the damped/driven cubic NLS equation on the torus of a large period $L$ with a small nonlinearity of size $\lambda$, a properly scaled random forcing and dissipation. We examine its solutions under the subsequent limit when…
We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid, in the temperature regime where the normal fluid density $\rho_n(T)$ is small. The coupling between the vortex "zero mode" and the…
The dynamics of one and two pointlike vortices in a planar quantum gas of spin-0 particles confined in an annular region is considered. New analytical and numerical solutions are found. The concept of stationarity radius, related to the…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
The global asymptotic dynamics of point vortices for the lake equations is rigorously derived. Vorticity that is initially sharply concentrated around $N$ distinct vortex centers is proven to remain concentrated for all times. Specifically,…
We consider the evolution and dissipation of vortex rings in a condensate at non-zero temperature, in the context of the classical field approximation, based on the defocusing nonlinear Schr\"odinger equation. The temperature in such a…
The superfluid flow velocity is proportional to the gradient of the phase of the superfluid order parameter, leading to the quantization of circulation around a vortex core. In this work, we study the dynamics of a superfluid film on the…
Turbulence in inviscid quantum fluids offers unparalleled access to the universal principles of non-equilibrium dynamics, spanning a vast range of length scales from macroscopic flow down to the individual vortex core. In the…
Vortices in fluids and superfluids are fundamental to phenomena ranging from Bose-Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where background geometry often plays an important role. Curvature…
We discuss the statistical properties of a single vortex line in a perfect fluid. The partition function is calculated up to the end in the thin vortex approximation. It turns out that corresponding theory is renormalizable, and the…
Through the Ginzburg-Landau and the Navier-Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of…