Integer, fractional, and anomalous quantum Hall effects explained with Eyring's rate process theory and free volume concept

Abstract

The Hall effects, especially the integer, fractional and anomalous quantum Hall effects, have been addressed using Eyring's rate process theory and free volume concept. The basic assumptions are that the conduction process is a common rate controlled "reaction" process that can be described with Eyring's absolute rate process theory; the mobility of electrons should be dependent on the free volume available for conduction electrons. The obtained Hall conductivity is clearly quantized as with prefactors related to both the magnetic flux quantum number and the magnetic quantum number via the azimuthal quantum number, with and without an externally applied magnetic field. This article focuses on two dimensional (2D) systems, but the approaches developed in this article can be extended to 3D systems.

Dislocation phenomena described with free volume concept and Eyring's rate process theory

“…10,11 Dislocation should still be a thermally driven process and follow the thermodynamic laws. One of the authors in this article has integrated the free volume concept with Eyring's rate process theories to theoretically interpret many seemingly unrelated phenomena ranging from electrical conductivity, 12 Hall effect, 13 superconductivity, 14,15 viscosities of colloidal suspensions, polymers, and glassing liquids, 16,17 to the flowability of granular matter, [18][19][20][21] etc. The universality and broad applications of this theory make us believe that it is capable of describing the dislocation phenomena widely observed among many kinds of materials, even large-scale geological entities.…”

Infection Dynamics of Coronavirus Disease 2019 (Covid-19) Modeled with the Integration of the Eyring’s Rate Process Theory and Free Volume Concept

“…All different kinds of interactions among entities are factored into a single term, the free volume available in a system. Since the free volume theory resolves how large freedom an entity may have and the Eyring’s rate process theory describes how fast the process is, these two theories have been integrated together to describe many seemingly unrelated systems or phenomena like glass liquids 12 , colloids and polymers 14,15 , granules 16–18 , electrical and proton conductivity 19,20 , superconductivity 21 , and Hall Effect 22 with great success.…”

Prediction of Coronavirus Disease (covid-19) Evolution in USA with the Model Based on the Eyring’s Rate Process Theory and Free Volume Concept

“…The Eyring’s rate process theory 9 argues that every physical or chemical phenomenon is a rate controlled process, while the free volume concept 10–14 argues that the transmission speed is also dependent on the available free volume. Many seemingly unrelated systems or phenomena can be successfully described with these two theories, such as glass liquids 13 , colloids and polymers 15,16 , granules 17–19 , electrical and proton conductivity 20,21 , superconductivity 22 , and Hall Effect 23 , etc. The infectious disease transmission phenomenon, a very complicated macroscopic process, could be properly analyzed with these two theories, too.…”