Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum Mechanics for Quantum Many-Body Systems: The Linear Response
  Regime   We derive a closed equation of motion for the current density of an
inhomogeneous quantum many-body system under the assumption that the
time-dependent wave function can be described as a geometric deformation of the
ground-state wave function. By describing the many-body system in terms of a
single collective field we provide an alternative to traditional approaches,
which emphasize one-particle orbitals. We refer to our approach as continuum
mechanics for quantum many-body systems. In the linear response regime, the
equation of motion for the displacement field becomes a linear fourth-order
integro-differential equation, whose only inputs are the one-particle density
matrix and the pair correlation function of the ground-state. The complexity of
this equation remains essentially unchanged as the number of particles
increases. We show that our equation of motion is a hermitian eigenvalue
problem, which admits a complete set of orthonormal eigenfunctions under a
scalar product that involves the ground-state density. Further, we show that
the excitation energies derived from this approach satisfy a sum rule which
guarantees the exactness of the integrated spectral strength. Our formulation
becomes exact for systems consisting of a single particle, and for any
many-body system in the high-frequency limit. The theory is illustrated by
explicit calculations for simple one- and two-particle systems.

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The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat