Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Det-Det Correlations for Quantum Maps: Dual Pair and Saddle-Point
  Analyses   An attempt is made to clarify the ballistic non-linear sigma model formalism
recently proposed for quantum chaotic systems, by the spectral determinant
Z(s)=Det(1-sU) of a quantized map U element of U(N). More precisely, we study
the correlator omega_U(s)=<|Z(st)|^2> (averaging t over the unit circle).
Identifying the group U(N) as one member of a dual pair acting in the spinor
representation of Spin(4N), omega_U(s) is expanded in terms of irreducible
characters of U(N). In close analogy with the ballistic non-linear sigma model,
a coherent-state integral representation of omega_U(s) is developed. We show
that the leading-order saddle-point approximation reproduces omega_U(s)
exactly, up to a constant factor; this miracle can be explained by interpreting
omega_U(s) as a character of U(2N), for which the saddle-point expansion yields
the Weyl character formula. Unfortunately, this decomposition behaves
non-smoothly in the semiclassical limit, and to make further progress some
averaging over U needs to be introduced. Several averaging schemes are
investigated. In general, a direct application of the saddle-point
approximation to these schemes is demonstrated to give incorrect results; this
is not the case for a `semiclassical averaging scheme', for which all loop
corrections vanish identically. As a side product of the dual pair
decomposition, we compute a crossover between the Poisson and CUE ensembles for
omega_U(s).

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The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: quant-ph