Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model

Abstract

Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral stability criterion and the formal stability criterion in the form of necessary and sufficient conditions. These criteria determine stability of spatially inhomogeneous solutions whose stability has not been decided correctly by using a less refined formal stability criterion. It is shown that some of such solutions can be found in a family of stationary solutions to the Vlasov equation, which is parametrized with macroscopic quantities and has a two-phase coexistence region in the parameter space.

17 pages, 4 figures, text modified, section VE added, references added, Accepted for publication in Phys. Rev. E

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Lynden-Bell and Tsallis distributions for the HMF model

Cited by in corpus (6)

• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics
• Trapping scaling for bifurcations in Vlasov systems
• General linear response formula for non integrable systems obeying the Vlasov equation
• Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions
• Nonlinear instability of inhomogeneous steady states solutions to the HMF Model