Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

Dipankar Roy; Abhishek Dhar; Konstantin Khanin; Manas Kulkarni; Herbert Spohn

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arXiv · 2401.06399

Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

Dipankar Roy·Abhishek Dhar·Konstantin Khanin·Manas Kulkarni·Herbert Spohn

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Abstract

In our contribution we study stochastic models in one space dimension with two conservation laws. One model is the coupled continuum stochastic Burgers equation, for which each current is a sum of quadratic non-linearities, linear diffusion, and spacetime white noise. The second model is a two-lane stochastic lattice gas. As distinct from previous studies, the two conserved densities are tuned such that the flux Jacobian, a $2 \times 2$ matrix, has coinciding eigenvalues. In the steady state, investigated are spacetime correlations of the conserved fields and the time-integrated currents at the origin. For a particular choice of couplings the dynamical exponent 3/2 is confirmed. Furthermore, at these couplings, continuum stochastic Burgers equation and lattice gas are demonstrated to be in the same universality class.

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Dipankar Roy, Abhishek Dhar, Konstantin Khanin, Manas Kulkarni, Herbert Spohn. 2024-01-12. Universality in coupled stochastic Burgers systems with degenerate flux Jacobian. https://arxiv.org/abs/2401.06399

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