Enhanced particle diffusion in fluctuating binary environments

We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquidlike) and high-friction (glassylike) states. The dynamics are governed by the ratio between the friction switching time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>τ</a:mi> </a:math> and the intrinsic velocity relaxation time <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>τ</b:mi> <b:mn>0</b:mn> </b:msub> </b:math> . For fast switching ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>τ</c:mi> <c:mo>/</c:mo> <c:msub> <c:mi>τ</c:mi> <c:mn>0</c:mn> </c:msub> <c:mo>≲</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> ), the motion is homogeneous and Brownian, whereas for slow switching ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>τ</d:mi> <d:mo>/</d:mo> <d:msub> <d:mi>τ</d:mi> <d:mn>0</d:mn> </d:msub> <d:mo>≫</d:mo> <d:mn>1</d:mn> </d:mrow> </d:math> ) the particle exhibits intermittent dynamics and an enhanced diffusion coefficient. Analysis of the single-particle overlap function <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>Q</e:mi> <e:mo>(</e:mo> <e:mi>t</e:mi> <e:mo>)</e:mo> </e:mrow> </e:math> and the dynamic susceptibility <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>χ</f:mi> <f:mn>4</f:mn> </f:msub> <f:mrow> <f:mo>(</f:mo> <f:mi>t</f:mi> <f:mo>)</f:mo> </f:mrow> </f:mrow> </f:math> reveals decoupling of the diffusion coefficient from the average friction upon cooling, which coincides with increasing temporal dynamic heterogeneity. This minimal model provides a transparent framework for understanding single-particle transport in media with temporally fluctuating local mobility and intermittent fast/slow dynamical regimes.