Matrix generalizations of some dynamic field theories

Abstract

We introduce matrix generalizations of the Navier--Stokes (NS) equation for fluid flow, and the Kardar--Parisi--Zhang (KPZ) equation for interface growth. The underlying field, velocity for the NS equation, or the height in the case of KPZ, is promoted to a matrix that transforms as the adjoint representation of $SU(N)$. Perturbative expansions simplify in the $N\to \infty$ limit, dominated by planar graphs. We provide the results of a one--loop analysis, but have not succeeded in finding the full solution of the theory in this limit.

9 pages, Hard copy figures available from: [email protected]

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• Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
• Correlation Functions in Disordered Systems
• Scaling Exponents for Kinetic Roughening in Higher Dimensions
• Glassy Solutions of the Kardar-Pasrisi-Zhang Equation
• Slow Relaxation in a Model with Many Conservation Laws : Deposition and Evaporation of Trimers on a Line

Cited by in corpus (6)

• Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers
• Random interface growth in random environment: Renormalization group analysis of a simple model
• The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
• Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
• Non equilibrium statistical physics with fictitious time
• Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment