相关论文: Asymptotic Stability of the Landau-Lifshitz Equati…
Experiments in spintronics and magnonics operate with macroscopically large number of localized spins within ferromagnetic (F) or antiferromagnetic (AF) materials, so that their nonequilibrium dynamics is standardly described by the…
We pursue our work on the asymptotic regimes of the Landau-Lifshitz equation for bi-axial ferromagnets. We put the focus on the cubic Schr{\"o}dinger equation, which is known to describe the dynamics in a regime of strong easy-axis…
Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d…
The Landau--Lifshitz--Bloch equation perturbed by a space-dependent noise was proposed in Garanin 1991 as a model for evolution of spins in ferromagnatic materials at the full range of temperatures, including the temperatures higher than…
The Landau--Lifshitz--Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we…
We prove the asymptotic stability in the energy space of non-zero speed solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. More precisely, we show that any solution corresponding to an initial datum…
We examine the stability of vortex-like configuration of magnetization in magnetic materials, so-called the magnetic skyrmion. These correspond to critical points of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya (DM)…
The Landau-Lifshitz-Gilbert damping coefficient employed in the analysis of spin wave ferromagnetic resonance is related to the electrical conductivity of the sample. The changing magnetization (with time) radiates electromagnetic fields.…
The interaction of coherent magnetization rotation with a system of two-level impurities is studied. Two different, but not contradictory mechanisms, the `slow-relaxing ion' and the `fast-relaxing ion' are utilized to derive a system of…
We construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems; Our description relies on the operator theoretic correlation inequalities. Within the new framework, we reinterpret…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is…
We propose that domain walls formed in a classical Ginzburg-Landau model can exhibit topologically stable but thermodynamically metastable states. This proposal relies on Allen-Cahn's assertion that the velocity of domain wall is…
Non-damped oscillations of the magnetization vector of a ferromagnetic system subject to a spin polarized current and an external magnetic field are studied theoretically by solving the Landau-Lifshitz-Gilbert equation. It is shown that the…
In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
Magnetization dynamics in ferromagnetic materials is modeled by the Landau-Lifshitz (LL) equation, a nonlinear system of partial differential equations. Among the numerical approaches, semi-implicit schemes are widely used in the…
We prove the existence and uniqueness of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with Dirichlet boundary condition for large anisotropies and small domains, where the domains are non-simply connected.
Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg-Landau equation (CGL), $$ \partial_t u = (a + i\alpha) \Delta u - (b + i \beta) |u|^\sigma u + k u, \,\,…
The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms,…