Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivative of the Lieb definition for the energy functional of density
  functional theory with respect to the particle number and the spin number   The nature of the explicit dependence on the particle number N and on the
spin number N_s of the Lieb definition for the energy density functional is
examined both in spin-free and in spin-polarized density functional theory.
First, it is pointed out that for ground states, the nonuniqueness of the
external magnetic field B(r) corresponding to a given pair of density n(r) and
spin density s(r) in spin-polarized density functional theory implies the
nonexistence of the derivative of the SDFT Lieb functional with respect to N_s.
Giving a suitable generalization of the Lieb functionals for n(r)'s and s(r)'s
with norms not equal to N and N_s of the functionals' subscripts, it is then
shown that the Lieb functionals' derivatives with respect to N and N_s are
equal to the derivatives, with respect to N and N_s, of the total energies
E[N,v] and E[N,N_s,v,B] minus the external-field energy components,
respectively.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol