Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free path lengths in quasicrystals   Previous studies of kinetic transport in the Lorentz gas have been limited to
cases where the scatterers are distributed at random (e.g. at the points of a
spatial Poisson process) or at the vertices of a Euclidean lattice. In the
present paper we investigate quasicrystalline scatterer configurations, which
are non-periodic, yet strongly correlated. A famous example is the vertex set
of the Penrose tiling. Our main result proves the existence of a limit
distribution of the free path length, which answers a question of Wennberg. The
limit distribution is characterised by a certain random variable on the space
of higher dimensional lattices, and is distinctly different from the
exponential distribution observed for random scatterer configurations. The key
ingredients in the proofs are equidistribution theorems on homogeneous spaces,
which follow from Ratner's measure classification.

7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex