d-Dimensional KPZ equation as a stochastic gradient flow in an evolving landscape : interpretation and time evolution of its generating functional
Date
2017Author
Wio, Horacio Sergio
Rodríguez, Miguel A.
Gallego, Rafael
Revelli, Jorge Alberto
Alés, Alejandro
Deza, Roberto Raúl
ORCID
https://orcid.org/0000-0001-6183-9617https://orcid.org/0000-0003-4184-0463
https://orcid.org/0000-0002-8277-6026
https://orcid.org/0000-0003-2135-3510
https://orcid.org/0000-0003-0812-3104
https://orcid.org/0000-0002-2469-3302
Metadata
Show full item recordAbstract
The deterministic KPZ equation has been recently formulated as a gradient flow. Its non-equilibrium analog of a free energy—the “non-equilibrium 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 to h(x,t) from some initial configuration h0(x,0). After pinpointing some implications of these facts, we study the time behavior of ⟨Φ[h]⟩t (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. 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.
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Wio, H. S., Rodríguez, M. A., Gallego, R., Revelli, J. A., Alés, A. y Deza, R. R. (2017). d-Dimensional KPZ equation as a stochastic gradient flow in an evolving landscape : interpretation and time evolution of its generating functional. Frontiers in Physics, 4. https://doi.org/10.3389/fphy.2016.00052