论文标题
概率的细胞自动机，用于量子粒子
Probabilistic cellular automaton for quantum particle in a potential
论文作者
论文摘要
我们提出，一个空间维度中电势中的量子粒子可以用概率的细胞自动机描述。虽然自动机的简单更新规则是确定性的，但概率描述是在初始条件下的概率分布引入的。提出的自动机涉及右和左移动者，从一个单元跳到一个相邻的单元格。他们改变了每个随机分布障碍或散射点的运动方向。无限数量的细胞的连续限量产生了dirac方程，在非相关性的限制中，熟悉的schrödinger方程，并由散射点的时空分布确定。这些方程描述了粒子位置的概率信息的时间演变。可观察到的所有量子规则，包括离散的可能的测量值和连续期望值，都遵循经典的统计定律。
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced by a probability distribution over initial conditions. The proposed automaton involves right- and left-movers, jumping from one cell to a neighboring one. They change their direction of motion at each randomly distributed disorder or scattering point. The continuum limit of an infinite number of cells yields a Dirac equation, and in the non-relativistic limit the familiar Schrödinger equation, with potential determined by the spacetime-distribution of scattering points. These equations describe the time evolution of the probabilistic information for the position of the particle. All quantum rules for observables, both for discrete possible measurement values and continuous expectation values, follow from the classical statistical laws.
