TY - JOUR

T1 - Field-Theoretic Renormalization Group in Models of Growth Processes, Surface Roughening and Non-Linear Diffusion in Random Environment: Mobilis in Mobili

AU - Антонов, Николай Викторович

AU - Гулицкий, Николай Михайлович

AU - Какинь, Полина Игоревна

AU - Лебедев, Никита Михайлович

AU - Тумакова, Мария Михайловна

PY - 2023/8/8

Y1 - 2023/8/8

N2 - This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum field theory that allows the application of the powerful methods of the latter to the study of stochastic systems. Then, we use the results of our recent research to illustrate several interesting effects of turbulent environment on the non-equilibrium critical behavior. Specifically, we couple the Kazantsev–Kraichnan “rapid-change” velocity ensemble that describes the environment to the three different stochastic models: the Kardar–Parisi–Zhang equation with time-independent random noise for randomly growing surface, the Hwa–Kardar model of a “running sandpile” and the generalized Pavlik model of non-linear diffusion with infinite number of coupling constants. Using field-theoretic renormalization group analysis, we show that the effect can be quite significant leading to the emergence of induced non-linearity or making the original anisotropic scaling appear only through certain “dimensional transmutation”.

AB - This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum field theory that allows the application of the powerful methods of the latter to the study of stochastic systems. Then, we use the results of our recent research to illustrate several interesting effects of turbulent environment on the non-equilibrium critical behavior. Specifically, we couple the Kazantsev–Kraichnan “rapid-change” velocity ensemble that describes the environment to the three different stochastic models: the Kardar–Parisi–Zhang equation with time-independent random noise for randomly growing surface, the Hwa–Kardar model of a “running sandpile” and the generalized Pavlik model of non-linear diffusion with infinite number of coupling constants. Using field-theoretic renormalization group analysis, we show that the effect can be quite significant leading to the emergence of induced non-linearity or making the original anisotropic scaling appear only through certain “dimensional transmutation”.

KW - cooperative systems

KW - critical behavior

KW - kinetic roughening

KW - random growth

KW - renormalizaton group

KW - scaling

KW - self-organized criticality

KW - universality

UR - https://www.mendeley.com/catalogue/3833b384-b61e-3eec-9e24-60d594a8fee1/

U2 - 10.3390/sym15081556

DO - 10.3390/sym15081556

M3 - Review article

VL - 15

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 8

M1 - 1556

ER -