标题： 量子力学的线性从哈密顿胞自动机的角度 显示英文标题

标题： The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

摘要： 我们讨论了一类最近引入的整数值胞状自动机[1]的作用原理及其导致的哈密顿运动方程。通过采样理论，这些确定性的有限差分方程被可逆地映射到描述一组带宽受限的简谐振子的连续方程上。它们代表薛定谔方程。然而，包含了反映带宽限制的修改，即存在一个时间（或长度）尺度。当这个离散尺度趋于零时，通常的结果会被得到。因此，量子力学的线性性质可以追溯到这类胞状自动机所假定的作用原理及其守恒律到离散的守恒律。胞状自动机的守恒律与相关的量子力学模型中的守恒律存在一一对应关系，而可允许的对称性则不然。 显示英文摘要

摘要： We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schroedinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.