d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional

Frontiers in Physics

Wio, Horacio S.¹  guez, Miguel A.¹  Deza, Roberto R.¹  Revelli, Jorge A.³  Alé⁴  s, Alejandro⁵  Rodrí⁹  Gallego, Rafael⁹ 

[1] Instituto de FíInstituto de Investigaciones FíMathematics Department, Gijón Campus, Universidad de Oviedo, Gijón, Spain;rdoba and CONICET, FaMAF-UNC, Córdoba, Argentina;sica Enrique Gaviola, Universidad Nacional de Cósica de Cantabria, Universidad de Cantabria and CSIC, Santander, Spain;sicas de Mar del Plata, Universidad Nacional de Mar del Plata and CONICET, FCEyN-UNMdP, Mar del Plata, Argentina

关键词: Nonequilibrium growth;    scaling laws;    Variational principles;    stochastic methods;    Interface roughening;   

DOI  :  10.3389/fphy.2016.00052

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

The deterministic KPZ equation has been recently formulated as a gradient flow. Its nonequilibrium analog of a free energy---the "nonequilibrium potential'' Φ[h], providing at each time the landscape where the stochastic dynamics of h(x ⃗,t) takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading from some initial configuration h(x ⃗,0) to a final one h(x ⃗,t). After pinpointing some implications of these facts, we study the time behavior of 〈Φ[h] 〉 (the average of Φ[h] over noise realizations at time t) and show the interesting consequences of its structure when an external driving force F is included (i.e. the KPZ behavior as an activation-like process). The asymptotic form of the time derivative Φ ̇[h] is shown to be valid for any substrate dimensionality d, thus providing a valuable tool for studies in d>1.

【 授权许可】

CC BY