Nonlinear Spin Dynamics in Nuclear Magnets

A method is developed for solving nonlinear systems of differential, or integrodifferential, equations with stochastic fields. The method makes it possible to give an accurate solution for an interesting physical problem: What are the peculiarities of nonlinear spin dynamics in nonequilibrium nuclear magnets coupled with a resonator? Evolution equations for nuclear spins are derived basing on a Hamiltonian with dipole interactions. The ensemble of spins is coupled with a resonator electric circuit. Seven types of main relaxation regimes are found: free induction, collective induction, free relaxation, collective relaxation, weak superradiance, pure superradiance, and triggered superradiance. The initial motion of spins can be originated by two reasons, either by an imposed initial coherence or by local spin fluctuations due to nonsecular dipole interactions. The relaxation regimes caused by the second reason cannot be described by the Bloch equations. Numerical estimates show good agreement with experiment.Comment: 1 file, 47 pages, LaTe

Asymptotic solutions to the first order differential equation with deviated argument and slowly varying coefficients

The object of this paper is to study the problem of constructing an approximate solution to the first order weakly nonlinear ordinary differential equation with deviated argument and slowly varying coefficients. Based on asymptotic techniques in nonlinear mechanics an algorithm for asymptotic integration of the differential equation under consideration is given.Розглядається задача про побудову наближених розв’язкiв слабконелiнiйного диференцiального рiвняння першого порядку з вiдхиленням аргументу i повiльно змiнними коефiцiєнтами. На основi асимптотичних методiв нелiнiйної механiки запропоновано алгоритм асимптотичного iнтегрування диференцiального рiвняння вказаного вище клас