TY - JOUR

T1 - Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise: Emergence of Induced Nonlinearity

AU - Какинь, Полина Игоревна

AU - Рейтер, Михаил Алексеевич

AU - Тумакова, Мария Михайловна

AU - Гулицкий, Николай Михайлович

AU - Антонов, Николай Викторович

N1 - Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/1/26

Y1 - 2022/1/26

N2 - We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f (t, x) is specified by the pair correlation function 〈 f (t, x) f (t ′, x ′)〉 ∝ δ (d) (x − x ′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε = 4 − d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.

AB - We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f (t, x) is specified by the pair correlation function 〈 f (t, x) f (t ′, x ′)〉 ∝ δ (d) (x − x ′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε = 4 − d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.

KW - Critical behaviour

KW - Kinetic roughening

KW - Renormalization group

KW - Turbulence

KW - MULTIFRACTALS

KW - FIELD-THEORY

KW - BEHAVIOR

KW - UPPER CRITICAL DIMENSION

KW - MODEL

KW - turbulence

KW - critical behaviour

KW - RENORMALIZATION-GROUP ANALYSIS

KW - SCALE PROPERTIES

KW - GROWTH

KW - kinetic roughening

KW - OPERATOR PRODUCT EXPANSION

KW - renormalization group

KW - DYNAMIC PHASE-TRANSITIONS

UR - http://www.scopus.com/inward/record.url?scp=85123759327&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b7fc4ac9-76b7-38c9-86a6-f5b170b2b4be/

U2 - 10.3390/universe8020072

DO - 10.3390/universe8020072

M3 - Article

VL - 8

JO - Universe

JF - Universe

SN - 2218-1997

IS - 2

M1 - 72

ER -