Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonequilibrium dynamics of superconductivity in the attractive Hubbard
  model   We present a framework of semiclassical superconductivity (SC) dynamics that
properly includes effects of spatial fluctuations for the attractive Hubbard
model. We consider both coherent and adiabatic limits. To model the coherent SC
dynamics, we develop a real-space von~Neumann equation based on the
time-dependent Hartree-Fock-Bogoliubov theory. Applying our method to
interaction quenches in the negative-$U$ Hubbard model, we show that the
relaxation of SC order at weak coupling is dominated by Landau-damping. At
strong coupling, we find a two-stage relaxation of the pairing field: a
collapse of the synchronized oscillation of Cooper pairs due to spatial
inhomogeneity, followed by a slow relaxation to a quasi-stationary state. SC
dynamics in adiabatic limit is described by a quantum Landau-Lifshitz equation
with Ginzburg-Landau relaxation. Numerical simulations of the pump-probe
process show that long time recovery of the pairing field is dominated by
defects dynamics. Our results demonstrate the important role of spatial
fluctuations in both limits.

13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat