TY - JOUR

T1 - Effect of Random Environment on Kinetic Roughening: Kardar–Parisi–Zhang Model with a Static Noise Coupled to the Navier–Stokes Equation

AU - Антонов, Николай Викторович

AU - Какинь, Полина Игоревна

AU - Рейтер, Михаил Алексеевич

PY - 2023/10/1

Y1 - 2023/10/1

N2 - Abstract: Kinetic roughening of a randomly growing surface can be modelled by the Kardar–Parisi–Zhang equation with a time-independent (“spatially quenched” or “columnar”) random noise. In this paper, we use the field-theoretic renormalization group approach to investigate how randomly moving medium affects the kinetic roughening. The medium is described by the stochastic differential Navier–Stokes equation for incompressible viscous fluid with an external stirring force. We find that the action functional for the full stochastic problem should be extended to be renormalizable: a new nonlinearity must be introduced. Moreover, in order to correctly reconcile dynamics of the scalar and velocity fields, a new parameter must be introduced as a factor in the covariant derivative of the scalar field. The resulting action functional involves four coupling constants and a dimensionless ratio of kinematic coefficients. The one-loop calculation (the leading order of the expansion in ε = 4 - d with d being the space dimension) shows that the renormalization group equations in the five-dimensional space of those parameters reveal a curve of fixed points that involves an infrared attractive segment for ε > 0 .

AB - Abstract: Kinetic roughening of a randomly growing surface can be modelled by the Kardar–Parisi–Zhang equation with a time-independent (“spatially quenched” or “columnar”) random noise. In this paper, we use the field-theoretic renormalization group approach to investigate how randomly moving medium affects the kinetic roughening. The medium is described by the stochastic differential Navier–Stokes equation for incompressible viscous fluid with an external stirring force. We find that the action functional for the full stochastic problem should be extended to be renormalizable: a new nonlinearity must be introduced. Moreover, in order to correctly reconcile dynamics of the scalar and velocity fields, a new parameter must be introduced as a factor in the covariant derivative of the scalar field. The resulting action functional involves four coupling constants and a dimensionless ratio of kinematic coefficients. The one-loop calculation (the leading order of the expansion in ε = 4 - d with d being the space dimension) shows that the renormalization group equations in the five-dimensional space of those parameters reveal a curve of fixed points that involves an infrared attractive segment for ε > 0 .

UR - https://www.mendeley.com/catalogue/18f42030-e8be-3624-992e-431b8576a0c5/

U2 - 10.1134/S1547477123050072

DO - 10.1134/S1547477123050072

M3 - Article

VL - 20

SP - 1078

EP - 1080

JO - Physics of Particles and Nuclei Letters

JF - Physics of Particles and Nuclei Letters

SN - 1547-4771

IS - 5

ER -