Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Liouville equation for flavour evolution of neutrinos and neutrino
  wave packets   We consider several aspects related to the form, derivation and applications
of the Liouville equation (LE) for flavour evolution of neutrinos. To take into
account the quantum nature of neutrinos we derive the evolution equation for
the matrix of densities using wave packets instead of Wigner functions. The
obtained equation differs from the standard LE by an additional term which is
proportional to the difference of group velocities. We show that this term
describes loss of the propagation coherence in the system. In absence of
inelastic collisions, the LE can be reduced to a single derivative equation
over a trajectory coordinate. Additional time and spacial dependence may steam
from initial (production) conditions. The transition from single neutrino
evolution to the evolution of a neutrino gas is considered.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex