Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cumulants associated with geometric phases   The Berry phase can be obtained by taking the continuous limit of a cyclic
product $-\mbox{Im} \ln \prod_{I=0}^{M-1} \langle \Psi_0({\boldsymbol
  \xi}_I)|\Psi_0({\boldsymbol \xi}_{I+1})\rangle$, resulting in the circuit
integral $i \oint \mbox{d}{\boldsymbol \xi} \cdot \langle \Psi_0({\boldsymbol
  \xi})|\nabla_{\boldsymbol \xi}|\Psi_0({\boldsymbol \xi}\rangle$. Considering
a parametrized curve ${\boldsymbol \xi}(\chi)$ we show that the product
$\prod_{I=0}^{M-1} \langle \Psi_0(\chi_I)|\Psi_0( \chi_{I+1})\rangle$ can be
equated to a cumulant expansion. The first contributing term of this expansion
is the Berry phase itself, the other terms are the associated spread, skew,
kurtosis, etc. The cumulants are shown to be gauge invariant. It is also shown
that these quantities can be expressed in terms of an operator.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an