Related papers: On the Gross-Pitaevskii evolution linearized aroun…
This Ph.D. thesis, prepared under the supervision of Prof. Alexander Olevskii, is concerned with some problems in two areas of Fourier Analysis: uniqueness theory of trigonometric expansions, and the theory of translation invariant…
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate…
This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses that grow or decay in time. Previously, King et al. (Phys. Rev. Fluids, 1, 2016, 073604:1-19) and Huber et al. (IMA…
We study the two-dimensional Ginzburg-Landau model of a neutral superfluid in the vicinity of the vortex unbinding transition. The model is mapped onto an effective interacting vortex gas by a systematic perturbative elimination of all…
We calculate the renormalized quartic vertex function of the Ginzburg-Landau model for a superconducting film in a magnetic field by summing an infinite subset of diagrams, the so-called parquet graphs. Using this non-perturbative solution,…
Dynamics of simplest vortex knots, unknots, and links of torus type inside an atomic Bose-Einstein condensate in anisotropic harmonic trap at zero temperature has been numerically simulated using three-dimensional Gross-Pitaevskii equation.…
We consider non-selfadjoint operators of the kind arising in linearized NLS and prove dispersive bounds for the time-evolution without assuming that the edges of the essential spectrum are regular. Our approach does not depend on any…
The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93}, 160406 (2004)] on the decay of a doubly quantized vortex imprinted in $^{23}% $Na condensates is analyzed by numerically solving the Gross-Pitaevskii equation.…
We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi regime, where a small parameter $\epsilon$…
For a Bose-Einstein condensate placed in a rotating trap and confined in the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas Fermi regime. We investigate an asymptotic development of the energy, the…
In the nineties, Klein, Majda and Damodaran have formally derived a simplified asymptotic motion law for the evolution of nearly parallel vortex filaments in the context of the three dimensional Euler equation for incompressible fluids. In…
We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…
We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg-Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, $\Gamma$-converge to…
In the approach of the effective field theory of modified gravity, we derive the equations of motion for linear perturbations in the presence of a barotropic perfect fluid on the flat isotropic cosmological background. In a simple version…
We establish an area growth estimate for solutions that are bounded from above of the Liouville equation $\Delta u+K e^{2u}=0$ with a positive pinched curvature $0<\lambda\leq K\leq\Lambda$. As an application, we provide a new proof of…
The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterium…
We study the growth of degrees in many autonomous and non-autonomous lattice equations defined by quad rules with corner boundary values, some of which are known to be integrable by other characterisations. Subject to an enabling…
For $N\leq34,$ we construct traveling waves with small speed for the Gross-Pitaevskii equation, by gluing $N(N+1)/2$ pairs of degree $\pm1$ vortices of the Ginzburg-Landau equation. The location of these vortices is symmetric in the plane…
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected…