Nonlinear response for external field and perturbation in the Vlasov system
Abstract
A nonlinear response theory is provided by use of the transient linearization method in the spatially onedimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a secondorder phase transition. We apply the theory to the Hamiltonian meanfield model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is the nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.
 Publication:

Physical Review E
 Pub Date:
 May 2014
 DOI:
 10.1103/PhysRevE.89.052114
 arXiv:
 arXiv:1402.4250
 Bibcode:
 2014PhRvE..89e2114O
 Keywords:

 05.20.Dd;
 05.70.Jk;
 46.40.Ff;
 Kinetic theory;
 Critical point phenomena;
 Resonance damping and dynamic stability;
 Condensed Matter  Statistical Mechanics;
 Physics  Plasma Physics
 EPrint:
 15 pages, 8 figures, accepted for publication in Phys. Rev. E, Lemma 2 is corrected