Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Index and Dynamics of Quantized Contact Transformations   Quantized contact transformations are Toeplitz operators over a contact
manifold $(X,\alpha)$ of the form $U_{\chi} = \Pi A \chi \Pi$, where $\Pi :
H^2(X) \to L^2(X)$ is a Szego projector, where $\chi$ is a contact
transformation and where $A$ is a pseudodifferential operator over $X$. They
provide a flexible alternative to the Kahler quantization of symplectic maps,
and encompass many of the examples in the physics literature, e.g. quantized
cat maps and kicked rotors. The index problem is to determine $ind(U_{\chi})$
when the principal symbol is unitary, or equivalently to determine whether $A$
can be chosen so that $U_{\chi}$ is unitary. We show that the answer is yes in
the case of quantized symplectic torus automorphisms $g$---by showing that
$U_g$ duplicates the classical transformation laws on theta functions. Using
the Cauchy-Szego kernel on the Heisenberg group, we calculate the traces on
theta functions of each degree N. We also study the quantum dynamics generated
by a general q.c.t. $U_{\chi}$, i.e. the quasi-classical asymptotics of the
eigenvalues and eigenfunctions under various ergodicity and mixing hypotheses
on $\chi.$ Our principal results are proofs of equidistribution of
eigenfunctions $\phi_{Nj}$ and weak mixing properties of matrix elements
$(B\phi_{Ni}, \phi_{Nj})$ for quantizations of mixing symplectic maps.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph