Ballistic space-time correlators of the classical Toda lattice

作者: Herbert Spohn

DOI: 10.1088/1751-8121/AB91D5

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摘要: The Toda lattice is an integrable system and its natural space-time stationary states are the generalized Gibbs ensembles (GGE). Of particular physical interest then correlations of conserved fields. To leading order they scale ballistically. We report on exact solution respective hydrodynamic equations linearized around a GGE as background state. Thereby we obtain concise formula for family scaling functions.

参考文章(34)
A. M. Perelomov, The Toda Lattice Integrable Systems of Classical Mechanics and Lie Algebras. pp. 193- 244 ,(1990) , 10.1007/978-3-0348-9257-5_4
A. Cuccoli, M. Spicci, V. Tognetti, R. Vaia, Dynamic correlations of the classical and quantum Toda lattices. Physical Review B. ,vol. 47, pp. 7859- 7868 ,(1993) , 10.1103/PHYSREVB.47.7859
Ioana Dumitriu, Alan Edelman, Matrix models for beta ensembles Journal of Mathematical Physics. ,vol. 43, pp. 5830- 5847 ,(2002) , 10.1063/1.1507823
C. Boldrighini, Y.M. Suhov, One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States Communications in Mathematical Physics. ,vol. 189, pp. 577- 590 ,(1997) , 10.1007/S002200050218
M. Hénon, Integrals of the Toda lattice Physical Review B. ,vol. 9, pp. 1921- 1923 ,(1974) , 10.1103/PHYSREVB.9.1921
P. Gruner-Bauer, F. G. Mertens, Excitation spectrum of the Toda lattice for finite temperatures European Physical Journal B. ,vol. 70, pp. 435- 447 ,(1988) , 10.1007/BF01312117
M. Jenssen, W. Ebeling, Distribution functions and excitation spectra of Toda systems at intermediate temperatures Physica D: Nonlinear Phenomena. ,vol. 141, pp. 117- 132 ,(2000) , 10.1016/S0167-2789(00)00025-7
Emmanuel Cépa, Dominique Lépingle, Diffusing particles with electrostatic repulsion Probability Theory and Related Fields. ,vol. 107, pp. 429- 449 ,(1997) , 10.1007/S004400050092