Local stationarity for lattice dynamics in the harmonic approximation
Dudnikova, T. V. ; Spohn, H.
arXiv, 0505031 / Harvested from arXiv
Text on arXiv
We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\epsilon^{-1}$. We establish two time regimes. For times of order $\epsilon^{-\gamma}$, $0<\gamma<1$, locally the measure converges to a Gaussian measure which is space-time stationary with a covariance inherited from the initial (in general, non-Gaussian) measure. For times of order $\epsilon^{-1}$ this local space covariance changes in time and is governed by a semiclassical transport equation.
Publié le : 2005-05-10
Classification:  Mathematical Physics 
@article{0505031,
     author = {Dudnikova, T. V. and Spohn, H.},
     title = {Local stationarity for lattice dynamics in the harmonic approximation},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505031}
}

Dudnikova, T. V.; Spohn, H. Local stationarity for lattice dynamics in the harmonic approximation. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505031/