Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Sub-Geometric Phases in Density Matrix   In this letter, the generalization of geometric phase in density matrix is
presented, we show that the extended sub-geometric phase have unified
expression whatever in adiabatic or nonadiabatic procedure, the relations
between them and the usual Berry phase or Aharonov-Anandan phase are
established. We also demonstrated the influence of sub-geometric phases on the
physical observables. Finally, our treatment is naturally used to investigate
the geometric phase in mixed state.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
2
The categories of this paper are: math
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas