相空间中的扩散过程与量子力学
Diffusion Processes in Phase Spaces and Quantum Mechanics
摘要：
研究了相空间中电荷分布的扩散过程。相应的电荷在力场中和随机场的作用下运动。有坐标和动量的扩散运动。在我们的模型中，电荷的内部状态由复矢量定义。相对于电荷的固有时间，矢量以很大的恒定角速度旋转。扩散过程的状态是相空间上的（复值）波函数。如同在量子力学中一样，我们假设对于波函数，叠加原理成立。扩散过程使来自相空间的不同点的内部状态的向量平均化。这个扩散过程的微分方程的建立和检查。我们证明了运动（由这个过程描述）分解成一个快速运动和一个缓慢的运动。快速运动将任意波函数简化为来自子空间的函数，该子空间的元素由坐标的复值函数参数化。慢运动发生在这个子空间，它是描述的薛定谔方程。对模型的参数进行了估计。快速运动的持续时间为$10^{-11}$ s量级。
英文摘要：
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model, an inner state of the charge is defined by a complex vector. The vector rotates with a great constant angular velocity with respect to the proper time of the charge. A state of the diffusion process is a (complex-valued) wave function on the phase space. As in quantum mechanics, we assume that, for the wave functions, the superposition principle holds. The diffusion process averages out vectors of inner states from different points of the phase space. A differential equation for this diffusion process is founded and examined. We demonstrate that the motion (described by this process) decomposes into a fast motion and a slow motion. The fast motion reduces an arbitrary wave function to a function from a subspace whose elements are parameterized by complex-valued functions of coordinates. The slow motion occurs in this subspace and it is described by the Schr\''odinger equation. The parameters of the suggested model are estimated. The duration of the fast motion is of order $10^{-11}$ s.
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