Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Dynamical Meaning of Spectral Dimensions   Time averaging over the trajectory of a wavepacket up to time T defines a
statistical operator (density matrix). The corresponding (Von Neumann) entropy
is proven to asymptotically increase with time like D.log T, with D the
Hausdorff dimension of the Local Density of States, at least if the latter
measure has good scaling properties. In more general cases, spectral upper and
lower bounds for the increase of entropy are given, in terms of the Hausdorff
and of the Fractal Dimension of the Local Density of States.

3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess