Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General linear response formula for non integrable systems obeying the
  Vlasov equation   Long-range interacting N-particle systems get trapped into long-living
out-of-equilibrium stationary states called quasi-stationary states (QSS). We
study here the response to a small external perturbation when such systems are
settled into a QSS. In the N to infinity limit the system is described by the
Vlasov equation and QSS are mapped into stable stationary solutions of such
equation. We consider this problem in the context of a model that has recently
attracted considerable attention, the Hamiltonian Mean Field (HMF) model. For
such a model, stationary inhomogeneous and homogeneous states determine an
integrable dynamics in the mean-field effective potential and an action-angle
transformation allows one to derive an exact linear response formula. However,
such a result would be of limited interest if restricted to the integrable
case. In this paper, we show how to derive a general linear response formula
which does not use integrability as a requirement. The presence of conservation
laws (mass, energy, momentum, etc.) and of further Casimir invariants can be
imposed a-posteriori. We perform an analysis of the infinite time asymptotics
of the response formula for a specific observable, the magnetization in the HMF
model, as a result of the application of an external magnetic field, for two
stationary stable distributions: the Boltzmann-Gibbs equilibrium distribution
and the Fermi-Dirac one. When compared with numerical simulations, the
predictions of the theory are very good away from the transition energy from
inhomogeneous to homogeneous states.

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The categories of this paper are: physics
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The categories of this paper are: cs
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg