论文标题
在存在变化的磁场的情况下，Smoluchowski-Kramers近似的平均方法
An averaging approach to the Smoluchowski-Kramers approximation in the presence of a varying magnetic field
论文作者
论文摘要
我们研究了描述一个小质量$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $的平面运动的方程的小质量极限，其中包含一个由随机项扰动的磁成分。我们通过添加强度$ \ e> 0 $的小摩擦来使问题正常。我们表明，对于所有小而固定的摩擦，$ q_ {μ，\ e} $的小质量限制将解决方案$ q_ \ e $提供给随机一阶方程，其中包含噪声引起的漂移项。然后，通过使用Freidlin和Wentzell的经典平均定理对哈密顿系统的平均定理的概括，我们采用了运动$ q_ \ e $的慢速组件的限制，我们证明它通过在磁场强度强度强度强度的相同级别的级别连接组件中识别所有点的连接组件中所获得的所有点所获得的Markov过程薄弱地收敛到Markov过程。
We study the small mass limit of the equation describing planar motion of a charged particle of a small mass $μ$ in a force field, containing a magnetic component, perturbed by a stochastic term. We regularize the problem by adding a small friction of intensity $\e>0$. We show that for all small but fixed frictions the small mass limit of $q_{μ, \e}$ gives the solution $q_\e$ to a stochastic first order equation, containing a noise-induced drift term. Then, by using a generalization of the classical averaging theorem for Hamiltonian systems by Freidlin and Wentzell, we take the limit of the slow component of the motion $q_\e$ and we prove that it converges weakly to a Markov process on the graph obtained by identifying all points in the same connected components of the level sets of the magnetic field intensity function.
