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

Emergent Quantum Mechanics 2013

物理学;力学

Elze, Hans-Thomas^1

Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy^1

关键词: Bandwidth limiteds;    Conservation law;    Continuum equation;    Dinger equation;    Hamiltonian equations;    Harmonic oscillators;    Quantum mechanical model;    Sampling theory;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/504/1/012004/pdf
DOI  :  10.1088/1742-6596/504/1/012004

学科分类：力学，机械学

来源: IOP

【 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 Schrodinger 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.