We consider enhanced diffusion for Brownian motion on a tilted periodic potential. Expressing the effective diffusion in terms of the eigenvalue band structure, we establish a connection between band gaps in the eigenspectrum and enhanced diffusion. We explain this connection for a simple cosine potential with a linear force and then generalize to more complicated potentials including one-dimensional potentials with multiple frequency components and nonseparable multidimensional potentials. We find that potentials with multiple band gaps in the eigenspectrum can lead to multiple maxima or broadening of the force-diffusion curve. These features are likely to be observable in experiments.

中文翻译：

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倾斜周期势中布朗运动的增强扩散和特征值带结构

我们考虑在倾斜周期电势上布朗运动的增强扩散。用特征值带结构表达有效扩散，我们建立了特征谱带隙与增强扩散之间的联系。我们用线性力解释一个简单的余弦电势，然后将其推广到更复杂的电势，包括具有多个频率分量的一维电势和不可分的多维电势。我们发现，本征谱中具有多个带隙的势能会导致多重最大力或力扩散曲线变宽。这些功能可能在实验中可以观察到。