Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ehrenfest system and the rest point spectrum for a Hartree-type
  Equation   Following Ehrenfest's approach, the problem of quantum-classical
correspondence can be treated in the class of trajectory-coherent functions
that approximate as $\h\to 0$ a quantum-mechanical state. This idea leads to a
family of systems of ordinary differential equations, called Ehrenfest
M-systems (M=0,1,2,...), formally equivalent to the semiclassical approximation
for the linear Schroedinger equation.
  In this paper a similar approach is undertaken for a nonlinear Hartree-type
equation with a smooth integral kernel. It is demonstrated how quantum
characteristics can be retrieved directly from the corresponding Ehrenfest
systems, without solving the quantum equation: the semiclassical asymptotics
for the spectrum are obtained from the rest point solution. One of the key
steps is derivation of a modified nonlinear superposition principle valid in
the class of trajectory-coherent quantum states.

36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ