Random ballistic growth and diffusion in symmetric spaces

A. Gorsky (1) , S. Nechaev (2) , R. Santachiara (2, 3) , G. Schehr (4)

1 ITEP - Institute of Theoretical and Experimental Physics [Moscow]
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 J.-V. Poncelet Laboratory
4 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N-column box is described as a time-ordered product of N x N-matrices consisting of a single sl_2-block which has a random position along the diagonal. We show that the joint distribution of heights in a uniform BD process is described by the diffusion equation with Toda Hamiltonian. The group-theoretic structure of the system and links to some random matrix models are also discussed.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

A. Gorsky, S. Nechaev, R. Santachiara, G. Schehr. Random ballistic growth and diffusion in symmetric spaces. Nucl. Phys. B, 2012, 862, pp.167-192. ⟨10.1016/j.nuclphysb.2012.04.005⟩. ⟨hal-00633537⟩