Related papers: Infinite energy solutions to vortex equations gove…
An existence theory is established for a coupled non-linear elliptic system, known as "vortex equations", describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the…
In this paper, we establish existence of solutions to an indefinite coupled non-linear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both…
We study the vortex solutions in a multicomponent Zhang-Hansson-Kivelson model for the fractional quantum Hall effect, at the self-dual point. Vortices with minimal free energy represent Laughlin quasiholes. We find at least two classes of…
We prove the existence of infinitely many radial solutions for elliptic systems in Rn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…
The hydrodynamic equations with quantum effects are studied in this paper. First we establish the global existence of smooth solutions with small initial data and then in the second part, we establish the convergence of the solutions of the…
Vortex solutions in $U(1)\times U(1)$ Chern-Simons theory coupled to a pair of hard-core bosons representing two layers of electrons are analysed. It is shown that there is such a range of parameters $(\alpha\beta<\gamma^{2})$ in which…
We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq…
We study electronic structures of quasi-two-dimensional finite electron systems in high magnetic fields. The solutions in the fractional quantum Hall regime are interpreted as quantum liquids of electrons and off-electron vortices. The…
This work concerns the semilinear wave equation in three space dimensions with a power-like nonlinearity which is greater than cubic, and not quintic (i.e. not energy-critical). We prove that a scale-invariant Sobolev norm of any…
Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the…
In the Fractional Quantum Hall state, we introduce a bi-local mean field and get vortex mean field solutions. Rotational invariance is imposed and the solution is constructed by means of numerical self-consistent method. It is shown that…
This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…
As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…
Based on the $\phi$-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It is revealed that there exist…
We are concerned with the two-power nonlinear Schr\"odinger-type equations with non-local terms. We consider the framework of Sobolev-Lorentz spaces which contain singular functions with infinite-energy. Our results include global…
We establish the existence of spinning $Q$-vortex solitons in a complex scalar field theory with a sextic potential on a finite domain. By reducing the governing equation to a nonlinear boundary value problem, we use variational methods to…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…
Laughlin's Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with ``exotic'' the two-fold central extension of the planar Galilei group. The reduced system is identical to the one used to…