Related papers: Decay and Scattering for the Chern-Simons-Schr\"od…
The Cauchy problem for the Schr\"odinger equations is studied with time-dependent potentials growing polynomially in the spatial direction. First the existence and the uniqueness of solutions are shown in the weighted Sobolev spaces. In…
We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in…
We obtain almost-sure scattering for the cubic defocusing Schr{\"o}dinger equation in the Euclidean space {$\mathbb{R}^3$}, with randomized radially-symmetric initial data at some supercritical regularity scales. Since we make no smallness…
We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with N=2 supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the…
The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and…
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schr\"odinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main…
A practical method to solve cut-off Coulomb problems of two-cluster systems in the momentum space is given. When a sharply cut-off Coulomb force with a cut-off radius $\rho$ is introduced at the level of constituent particles, two-cluster…
In this short note, we prove a decay estimate for non-linear solutions of 3D cubic defocusing non-linear Schr\"odinger equation.
A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.
The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this…
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space $H^1(\mathbb{R})…
It has been shown in [Yang-Yu 2019] that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space $\mathbb{R}^{1+3}$ decay like linear solutions. One hence can define the associated…
We derive the long-time decay in weighted norms for solutions of the discrete 3D Schr\"odinger and Klein-Gordon equations.
We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to…
In this paper we investigate the Cauchy problem for Schr\"odinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^\infty$ well-posedness in the very weak sense under suitable assumptions of the…
For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related…
The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly…
We consider the Cauchy problem for the nonlinear Schr\"odinger equation with double nonlinearities with opposite sign, with one term is mass-critical and the other term is mass-supercritical and energy-subcritical, which includes the famous…
In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is convolved with the Coulomb potential 1/|x|, and it produces the long-range interaction…