# Slow relaxation in long-range interacting systems with stochastic dynamics.

@article{Gupta2010SlowRI, title={Slow relaxation in long-range interacting systems with stochastic dynamics.}, author={Shamik Gupta and David Mukamel}, journal={Physical review letters}, year={2010}, volume={105 4}, pages={ 040602 } }

Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to nondeterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian mean-field model, to include energy-conserving…

## 22 Citations

Relaxation dynamics of stochastic long-range interacting systems

- Physics
- 2010

Long-range interacting systems, while relaxing towards equilibrium, may get trapped in nonequilibrium quasistationary states (QSS) for a time which diverges algebraically with the system size. These…

Quasistationarity in a model of classical spins with long-range interactions

- Physics
- 2011

Systems with long-range interactions, while relaxing towards equilibrium, sometimes get trapped in long-lived non-Boltzmann quasistationary states (QSS) which have lifetimes that grow algebraically…

Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces.

- Medicine, PhysicsPhysical review. E
- 2019

Inspired by one-dimensional light-particle systems, the dynamics of a non-Hamiltonian system with long-range forces is investigated and it is implied that on a macroscopic scale the molecular dynamics evolves on a slow timescale that diverges with the system size.

Noise-induced dynamical phase transitions in long-range systems.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

It is shown that the presence of external noise sources can reduce their lifetime and induce at a specific time a dynamical phase transition marked by a nonzero order parameter that may be used as a distinctive experimental signature of the temporary existence of nonequilibrium Vlasov-stable states.

Quasistationarity in a model of long-range interacting particles moving on a sphere.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The model is found to exhibit long-lived nonmagnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized.

Self-consistent inhomogeneous steady states in Hamiltonian mean-field dynamics.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

This work proposes a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field, and shows numerically that the relaxation time of these states diverges with N with the exponent γ= 1.7.

Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is shown that the scalings discussed in the literature are mainly due to small size effects or the use of unsuitable variables to describe the dynamics, and the scaling obtained is proportional to the square of the number of particles.

Synchronized states of one dimensional long-range systems induced by inelastic collisions

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

We report results of numerical experiments which show that a family of simple one dimensional particle systems with long-range interactions, when subjected to a certain class of inelastic…

Phase transitions in systems with non-additive long-range interactions

- Physics, Mathematics
- 2013

We consider spin systems with long-range interactions in a non-additive regime. When the non-additive scaling limit is employed, the energy and the entropy compete and the system exhibits some phase…

Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence toward equilibrium of mean-field systems due to finite-N effects. The…

## References

SHOWING 1-10 OF 39 REFERENCES

Relaxation times of unstable states in systems with long range interactions

- Physics
- 2007

We consider several models with long range interactions evolving via Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian mean field (HMF) model and perturbed HMF models with…

Breaking of ergodicity and long relaxation times in systems with long-range interactions.

- Physics, MedicinePhysical review letters
- 2005

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the…

SUPERDIFFUSION AND OUT-OF-EQUILIBRIUM CHAOTIC DYNAMICS WITH MANY DEGREES OF FREEDOMS

- Physics
- 1999

We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body Hamiltonian system with long-range interaction showing a second-order phase…

Incomplete equilibrium in long-range interacting systems.

- Physics, MedicinePhysical review letters
- 2006

It is found that the central limit theorem implies the Boltzmann expression in Gibbs' Gamma space, and the nonequilibrium submanifold of Gamma space characterizing the anomalous behavior is identified, and by restricting the BoltZmann-Gibbs approach to this sub manifold the statistical mechanics of the quasistationary states are obtained.

Hamiltonian dynamics reveals the existence of quasistationary states for long-range systems in contact with a reservoir.

- Physics, MedicinePhysical review letters
- 2006

The dynamics confirms statistical mechanics equilibrium predictions for the Hamiltonian mean field model and the equilibrium ensemble equivalence and finds that long-lasting quasistationary states persist in the presence of the interaction with the environment.

Non-Gaussian equilibrium in a long-range Hamiltonian system.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

If the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions, Lévy walks, and dynamical correlation in phase space.

Microcanonical quasistationarity of long-range interacting systems in contact with a heat bath.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The identification of the key parameters determining the quasistationary lifetimes could be exploited to control experimental systems such as the free-electron laser, in the presence of external noise or inherent imperfections.

Dynamics and thermodynamics of systems with long‐range interactions: interpretation of the different functionals

- Physics
- 2008

We discuss the dynamics and thermodynamics of systems with weak long‐range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a…

Large Deviation Techniques Applied to Systems with Long-Range Interactions

- Mathematics, Physics
- 2005

AbstractWe discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D133:106…

Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This work explains the ubiquity and extremely slow evolution of non-Gaussian out-of-equilibrium distributions for the Hamiltonian mean-field model, and unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation.