Journal of Statistical Mechanics: Theory and Experiment, Volume (15), No (1), Year (2015-2) , Pages (1-20)

Title : ( Quantum mechanics used for modeling macroscopic structural systems: finite-element static analysis of a simple bar by the concepts in quantum mechanics )

Authors: Mehdi Khajavi , Reza Khajavi ,

Citation: BibTeX | EndNote

Abstract

In this paper, the two following fundamental questions in solid mechanics are answered by extending quantum-mechanical rules to macro level: 1. Why cannot both kinetic and kinematic quantities be known on a boundary point? 2. How does kinematic boundary data transfer over the continuum? For this purpose, the simple two-node bar finite element is introduced as a two-level quantum system (qubit); hence, two bar elements which are attached in series constitute an entangled two-qubit system. When a nodal or internodal kinetic/kinematic boundary condition (BC) is established (i.e. a quantum measurement is performed), the system collapses in a new state. A simple bar (discretized by finite element method) might thus be considered as a set of some entangled two-element systems, which successively collapse in new states when kinetic/kinematic BCs are consecutively applied. Through such a process, boundary kinetic/kinematic information transfer along the whole bar and the static analysis is implemented.

Keywords

, matrix models, elasticity (theory), entanglement in extended quantum systems (theory)