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Ballistic deposition model

NNN case

With S.Nechaev, R.Santachiara, G. Schehr


Elementary act of the deposition in the matrix form


It is the description of the whole heap



Let us consider the following anzatz

We get the following equation


The BD process as Markov process on the local semigroup with nontrivial local relations


Schematic realization of the BD problem

Diffusion equation reduces to the Toda system


The system asquires the form of the Toda chain in the rank 2 matrix formulation. However there is equivalent rank N Toda formulation which corresponds to the free motion on the symmetric space.

Geometrically it corresponds to the rotation of the «brane configuration»


The disordered wires system(Calogero model)

where


There is so called Inozemtsev limit when hyperbolic Calogero system gets reduced to the Toda chain

The corresponding limit in the statistical models corresponds to the relation betweem the transmission in the disordered wires (Calogero model) and ballistic deposition problem with SL(2,R) uniform multi-column box