Related papers: Analysis of a coupled spin drift-diffusion Maxwell…
The stochastic Landau--Lifshitz--Gilbert (LLG) equation coupled with the Maxwell equations (the so called stochastic MLLG system) describes the creation of domain walls and vortices (fundamental objects for the novel nanostructured magnetic…
Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of \vec S (\vec…
Coupled spin-charge drift-diffusion equations are derived for a biased two-dimensional electron gas with weak Rashba spin-orbit interaction. The basic equations formally agree with recent results obtained for spin-orbit coupled small…
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis…
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite…
We develop a general scheme of deriving boundary conditions for spin-charge coupled transport in disordered systems with spin-orbit interactions. To illustrate the application of the method, we explicitly derive boundary conditions for spin…
We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long wavelength limit. We find that the magnetization of the condensate is described by a non-trivial modification of the Landau-Lifshitz…
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the…
In this paper, we prove the global existence of solutions to the relativistic Vlasov-Poisson system for general initial data in convex bounded domains of two space dimensions, assuming the specular reflection boundary conditions for the…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
A semiclassical method is used to study Landau damping of transverse pseudo-spin waves in harmonically trapped ultracold gases in the collisionless Boltzmann limit. In this approach, the time evolution of a spin is calculated numerically as…
We consider a perturbed Stokes system with critical divergence-free drift in a bounded Lipschitz domain in $R^2$, with sufficiently small Lipschitz constant L. It extends our previous work in $\Bbb R^n, n\ge 3$, to two-dimensional case. For…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
Non-perturbative constraints on many body physics--such as the famous Lieb-Schultz-Mattis theorem--are valuable tools for studying strongly correlated systems. To this end, we present a number of non-perturbative results that constrain the…
Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for…
We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely…
The current-induced magnetisation dynamics in a ferromagnet at elevated temperatures can be described by the Landau--Lifshitz--Bloch (LLB) equation with spin-torque terms. In this paper, we focus on the regime above the Curie temperature.…
We prove the existence and uniqueness of global finite energy solutions of the Maxwell-scalar field system in Lorenz gauge on the Einstein cylinder. Our method is a combination of a conformal patching argument, the finite energy existence…
The solutions of the Landau-Lifshitz equation with finite-gap behavior at infinity are considered. By means of the inverse scattering method the large-time asymptotics is obtained.
We study the relaxation of a spin density injected into a two-dimensional electron system with generic spin-orbit interactions. Our model includes the Rashba as well as linear and cubic Dresselhaus terms. We explicitly derive a general…