Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion
  and conservation laws   We formulate equations of motion and conservation laws for a quantum
many-body system in a co-moving Lagrangian reference frame. It is shown that
generalized inertia forces in the co-moving frame are described by Green's
deformation tensor $g_{\mu\nu}(\bm\xi,t)$ and a skew-symmetric vorticity tensor
$\widetilde{F}_{\mu\nu}(\bm\xi,t)$, where $\bm\xi$ in the Lagrangian
coordinate. Equations of motion are equivalent to those for a quantum many-body
system in a space with time-dependent metric $g_{\mu\nu}(\bm\xi,t)$ in the
presence of an effective magnetic field $\widetilde{F}_{\mu\nu}(\bm\xi,t)$. To
illustrate the general formalism we apply it to the proof of the harmonic
potential theorem. As another example of application we consider a fast long
wavelength dynamics of a Fermi system in the dynamic Hartree approximation. In
this case the kinetic equation in the Lagrangian frame can be solved
explicitly. This allows us to formulate the description of a Fermi gas in terms
of an effective nonlinear elasticity theory. We also discuss a relation of our
results to time-dependent density functional theory.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas