Existence of Quasi-stationary states at the Long Range threshold

Abstract

In this paper the lifetime of quasi-stationary states (QSS) in the $\alpha -$HMF model are investigated at the long range threshold ($\alpha =1$). It is found that QSS exist and have a diverging lifetime $\tau (N)$ with system size which scales as $\mbox{\ensuremathτ(N)\ensuremath{\sim}}\log N$, which contrast to the exhibited power law for $\alpha <1$ and the observed finite lifetime for $\alpha >1$. Another feature of the long range nature of the system beyond the threshold ($\alpha >1$) namely a phase transition is displayed for $\alpha =1.5$. The definition of a long range system is as well discussed.

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems
• Lynden-Bell and Tsallis distributions for the HMF model
• Stationary states and fractional dynamics in systems with long range interactions
• Out of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field model
• Out of equilibrium phase transitions in mean field Hamiltonian dynamics

Cited by in corpus (4)

• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Vlasov equation for long-range interactions on a lattice
• Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model
• Emergence of a collective crystal in a classical system with long-range interactions