Purity dependent uncertainty relation and possible enhancement of quantum tunneling phenomenon

TL;DR

This paper explores how the purity of quantum states influences uncertainty relations and how decoherence can potentially enhance quantum tunneling by affecting barrier transparency.

Contribution

It introduces a purity-dependent uncertainty relation and analyzes how decoherence can modify quantum tunneling phenomena.

Findings

Barrier transparency $D$ relates to state purity $$ via $^{-1} ln D=const

For thermal states, barrier transparency depends on temperature as $T\ln D=const$

Decoherence processes can influence quantum tunneling by altering state purity

Abstract

The position-momentum uncertainty relations containing the dependence of their quantum bounds on state purity parameter $\mu$ are discussed in context of possibilities to influence on the potential barrier transparency by means of decoherence processes. The behavior of barrier transparency $D$ is shown to satisfy the condition $\mu^{-1}\ln D=const$. The particular case of thermal state with temperature $T$ where the purity parameter is a function of temperature is considered. For large temperature the condition for the barrier transparency is shown to be $T\ln D=const$.