Cooper Pair Formation by Quantizing Brownian Motion

Abstract

We derive a new quantum interaction by quantizing the Brownian motion based on the Nelson equations. By applying the canonical quantization for the equations, interaction as the connection of Brownian and quantum motions appears. Interesting aspect is that it can overcome the Coulomb repulsion if the diffusion coefficient is large enough. As the parameters are mass, diffusion coefficient, and probability density, we can calculate and predict the Cooper pair formation with measurable variables.

A Model connecting Quantum, Diffusion, Soliton, and Periodic Localized States under Brownian motion

“…here and hereafter, we assume the current velocity has no rotation. For a case s 1 = s 2 = 0, they coincide with the Nelson's equations, for s 2 = 0, they become the Davidson's equations [12], and for s 1 = s 2 = 1/2, they become the equations we proposed in previous paper [13]. The second equation is derived by the sum of two equations ( 4), then there is another independent equation.…”

“…Moreover, as is known that the limit → 0 recovers classical physics, choices of the parameter as s = 1/2 − 2 /2m 2 D 2 , s = 1/2, and s > 1/2 represent quantum, classical, and diffusion equations, respectively. Meanwhile, there is another extension of the Nelson equations with a different motivation [13]. We found a way to put them together in a framework of generalized equations of motion.…”