Brownian motion in a solitary potential well in a bounded solid structure

The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.