Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergence of Geometric phase shift in Planar Non-commutative Quantum
  Mechanics   Appearance of adiabatic geometric phase shift in the context of
noncommutative quantum mechanics is studied using an exactly solvable model of
2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity
are also considered along with spatial noncommutativity. After finding a
suitable Bopp shift, that bridges the noncommutative phase space operators with
their effective commutative counterparts, having their dependence on the
non-commutative parameters, we study the adiabatic evolution in the Heisenberg
picture. An explicit expression for the geometric phase shift under adiabatic
approximation is then found without using any perturbative technique. Lastly,
this phase is found to be related to the Hannay angle of a classically
analogous system, by studying the evolution of the coherent state of this
system.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol