2013/05/31 by Christian B. Mendl, Herbert Spohn · 139 citations
Mathematics · Physics and Astronomy · #Burgers' equation #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Conservation law #Conserved quantity #Coupling (piping) #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Mode coupling #Nonlinear Photonic Systems #Nonlinear system #Physics #Quadratic equation #Quantum mechanics #Statistical physics #Strong Light-Matter Interactions #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.111.230601
published in Physical Review Letters 111(23), 230601 (American Physical Society) · 2 figures
arxiv created 2013/11/11 · openalex publication_date 2013/12/03 · arxiv updated 2013/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact, our scheme is more general and would also cover other one-dimensional Hamiltonian systems, for example, classical and quantum fluids. Fluctuating hydrodynamics is a nonlinear system of conservation laws with noise. For a single mode, it is equivalent to the noisy Burgers equation, for which explicit solutions are available. Our focus is the case of several modes. No exact solution has been found so far, and we rely on a one-loop approximation. The resulting mode-coupling equations have a quadratic memory kernel and describe the time evolving 3×3 correlator matrix of the locally conserved fields. Long time asymptotics is computed analytically, and finite time properties are obtained through a numerical simulation of the mode-coupling equations.