A model violating the Boltzmann distribution

TL;DR

This paper investigates a quantum mechanical model of ionic conduction, revealing a violation of the classical Boltzmann distribution and offering an explanation for experimental Haven ratio anomalies.

Contribution

It introduces a quantum mechanical perspective to ionic conduction models, demonstrating a specific deviation from classical Boltzmann statistics.

Findings

Quantum mechanics causes a factor of 2 violation of Boltzmann distribution

The violation explains observed Haven ratio discrepancies

Classical mechanics aligns with Boltzmann distribution, quantum mechanics does not

Abstract

We study a model of an ionic conductor having interstitial ions that jump from site to site. The conductor is subject to an external electric field. According to classical mechanics, the ion number density follows the Boltzmann distribution. But according to quantum mechanics, we show that the Boltzmann distribution is violated by a factor of 2. And the violation provides a mechanism to explain the Haven ratio observed in some experiments.