Inviscid fixed point of the multidimensional Burgers-Kardar-Parisi-Zhang equation

Area of Science:

• Statistical physics
• Non-equilibrium systems
• Dynamical scaling

Background:

• Numerical simulations revealed a new z=1 dynamical critical exponent in 1D Kardar-Parisi-Zhang (KPZ) and noisy Burgers equations.
• This scaling differs from the standard KPZ z=3/2 and appears in tensionless/inviscid limits.

Purpose of the Study:

• To investigate the existence and properties of the inviscid Burgers (IB) fixed point in multidimensional Burgers-KPZ equations.
• To determine if the z=1 scaling regime extends to higher dimensions.

Main Methods:

• Functional renormalization group (FRG) analysis applied to the multidimensional Burgers-KPZ equation.
• Investigation of the fixed points and their stability in the inviscid limit.

Main Results:

• The inviscid Burgers (IB) fixed point is shown to exist in all dimensions d≥0.
• This IB fixed point controls the large momentum behavior of correlation functions in the inviscid limit.
• A super-universal dynamical exponent z=1 is found for all dimensions.

Conclusions:

• The newly discovered z=1 scaling regime is robust and extends to higher dimensions.
• The inviscid Burgers fixed point provides a universal description for these systems across dimensions.