Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual families of non-commutative quantum systems   We demonstrate how a one parameter family of interacting non-commuting
Hamiltonians, which are physically equivalent, can be constructed in
non-commutative quantum mechanics. This construction is carried out exactly (to
all orders in the non-commutative parameter) and analytically in two dimensions
for a free particle and a harmonic oscillator moving in a constant magnetic
field. We discuss the significance of the Seiberg-Witten map in this context.
It is shown for the harmonic oscillator potential that an approximate duality,
valid in the low energy sector, can be constructed between the interacting
commutative and a non-interacting non-commutative Hamiltonian. This
approximation holds to order 1/B and is therefore valid in the case of strong
magnetic fields and weak Landau-level mixing.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs