微观随机影响下的线性Hamilton系统
Linear Hamiltonian Systems under Microscopic Random Influence
摘要：
已知线性哈密顿系统具有太多的不变测度，因而收敛于Gibbs测度的问题没有意义。考虑任意有限维线性哈密顿系统，证明了在一个特殊坐标服从耗散和白噪声的条件下，对几乎任何哈密顿量和几乎任何初始条件，存在唯一的极限分布.此外，该分布是吉布斯分布，温度取决于白噪声的耗散和方差。
英文摘要：
It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite dimension and prove that, under the condition that one distinguished coordinate is subjected to dissipation and white noise, then, for almost any hamiltonians and almost any initial conditions, there exists the unique limiting distribution. Moreover, this distribution is Gibbsian with the temperature depending on the dissipation and of the variance of the white noise.
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