Ergodicity and central-limit theorem in systems with long-range interactions Export

@article{citeulike:4819995, abstract = {In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian mean-field model and show that the lifetime of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central-limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.}, author = {Figueiredo, A. and Filho, Rocha T. M. and Amato, M. A.}, citeulike-article-id = {4819995}, citeulike-linkout-0 = {http://dx.doi.org/10.1209/0295-5075/83/30011}, doi = {10.1209/0295-5075/83/30011}, journal = {EPL (Europhysics Letters)}, keywords = {central-limit-behavior, long-range-interactions}, number = {3}, pages = {30011+}, posted-at = {2009-06-12 05:15:18}, priority = {2}, title = {Ergodicity and central-limit theorem in systems with long-range interactions}, url = {http://dx.doi.org/10.1209/0295-5075/83/30011}, volume = {83}, year = {2008} }

TY - JOUR ID - citeulike:4819995 L3 - citeulike-article-id:4819995 N2 - In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian mean-field model and show that the lifetime of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central-limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution. IS - 3 JF - EPL (Europhysics Letters) TI - Ergodicity and central-limit theorem in systems with long-range interactions VL - 83 SP - 30011 KW - central-limit-behavior KW - long-range-interactions AU - Figueiredo, A AU - Filho, Rocha AU - Amato, MA PY - 2008/// UR - http://dx.doi.org/10.1209/0295-5075/83/30011 ER -