On the Cubic Lowest Landau Level Equation

Abstract

We study dynamical properties of the cubic lowest Landau level equation, which is used in the modeling of fast rotating Bose-Einstein condensates. We obtain bounds on the decay of general stationary solutions. We then provide a classification of stationary waves with a finite number of zeros. Finally, we are able to establish which of these stationary waves are stable, through a variational analysis.

43 pages

References in corpus (4)

• Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
• On the growth of Sobolev norms for NLS on $2d$ and $3d$ manifolds
• Bifurcations of multi-vortex configurations in rotating Bose--Einstein condensates
• Averaging of nonlinear Schrödinger equations with strong magnetic confinement

Cited by in corpus (22)

• Bounds on quantum evolution complexity via lattice cryptography
• Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
• Solvable cubic resonant systems
• Growth of Sobolev norms for coupled Lowest Landau Level equations
• Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
• Time-periodic quantum states of weakly interacting bosons in a harmonic trap
• Energy level splitting for weakly interacting bosons in a harmonic trap
• Complex plane representations and stationary states in cubic and quintic resonant systems
• Energy returns in global AdS_4
• Turbulent cascades in a truncation of the cubic Szego equation and related systems
• Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
• Breathing modes, quartic nonlinearities and effective resonant systems
• Melonic Turbulence
• Stationary states of the cubic conformal flow on ${\mathbb{S}}^3$
• Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems
• Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
• Bifurcations of multi-vortex configurations in rotating Bose--Einstein condensates
• Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials
• Phase-space localization at the lowest Landau level
• Energy cascades and condensation via coherent dynamics in Hamiltonian systems
• Vortex patterns of a two-dimensional Bose-Einstein condensate at the almost critical rotation speed
• A superintegrable quantum field theory