论文标题
多思素布朗系统与洛伦兹力的相关性
Correlations in multithermostat Brownian systems with Lorentz force
论文作者
论文摘要
我们研究由于外部磁场而受到洛伦兹力的布朗粒子的运动。粒子的每个空间自由度都耦合到不同的恒温器。我们表明，磁场会导致固定态不同速度成分之间的相关性。整合速度自相关矩阵时，我们获得了进入Fokker-Planck方程的扩散矩阵以达到概率密度。扩散矩阵的特征向量与温度轴不一致。结果，布朗粒子执行空间相关的扩散。我们进一步表明，在存在各向同性限制电势的情况下，出现了异常的，无通量的稳态，其特征在于非玻尔兹曼密度分布，可以通过逆转磁场来旋转。我们系统的非平凡稳态特性是由Lorentz力引起的空间自由度的耦合而导致的，而空间自由度的耦合停止在与单个温度系统相对应的平衡中存在。
We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion matrix that enters the Fokker-Planck equation for the probability density. The eigenvectors of the diffusion matrix do not align with the temperature axes. As a consequence the Brownian particle performs spatially correlated diffusion. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.
