Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonadiabatic extension of the Heisenberg model   The localized states within the Heisenberg model of magnetism should be
represented by best localized Wannier functions forming a unitary
transformation of the Bloch functions of the narrowest partly filled energy
bands in the metals. However, as a consequence of degeneracies between the
energy bands near the Fermi level, in any metal these Wannier functions cannot
be chosen symmetry-adapted to the complete paramagnetic group M^P. Therefore,
it is proposed to use Wannier functions with the reduced symmetry of a magnetic
subgroup M of M^P [case (a)] or spin dependent Wannier functions [case (b)].
The original Heisenberg model is reinterpreted in order to understand the
pronounced symmetry of these Wannier functions. While the original model
assumes that there is exactly one electron at each atom, the extended model
postulates that in narrow bands there are as many as possible atoms occupied by
exactly one electron. However, this state with the highest possible atomiclike
character cannot be described within the adiabatic (or Born-Oppenheimer)
approximation because in the (true) nonadiabatic system the electrons move on
localized orbitals that are still symmetric on the average of time, but not at
any moment. The nonadiabatic states have the same symmetry as the adiabatic
states and determine the commutation properties of the nonadiabatic Hamiltonian
H^n. The nonadiabatic Heisenberg model is a purely group- theoretical model
which interprets the commutation properties of H^n that are explicitly given in
this paper for the two important cases (a) and (b). There is evidence that the
occurrence of these two types of Wannier functions in the band structure of a
metal is connected with the occurrence of magnetism and superconductivity,
respectively.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
2
The categories of this paper are: math
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc