Yoshiyuki Y Yamaguchi et al J. Stat. Mech. (2007) P01020 doi:10.1088/1742-5468/2007/01/P01020
Algebraic correlation functions and anomalous diffusion in the Hamiltonian mean field model
Yoshiyuki Y Yamaguchi1, Freddy Bouchet2 and Thierry Dauxois3
Show affiliationsWe numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions in the quasi-stationary states of the Hamiltonian mean field model. This is an example, in an N-body Hamiltonian system, of anomalous transport properties characterized by non-exponential relaxations and long-range temporal correlations. Kinetic theory predicts a striking transition between weak anomalous diffusion and strong anomalous diffusion. The numerical results are in excellent agreement with the quantitative predictions of the anomalous transport exponents. It is noteworthy that, at statistical equilibrium also, the system exhibits long-range temporal correlations: the correlation function is inversely proportional to time with a logarithmic correction instead of the usually expected exponential decay, leading to weak anomalous transport properties.
- Keywords
- PACS
- MSC
- Subjects
- Dates
-
Issue 01 (January 2007)
Received 6 October 2006, accepted for publication 9 January 2007
Published 30 January 2007
-
Algebraic correlation functions and anomalous diffusion in the Hamiltonian mean field model
Yoshiyuki Y Yamaguchi et al J. Stat. Mech. (2007) P01020
-
Evidence for the super Tonks–Girardeau gas
M T Batchelor et al J. Stat. Mech. (2005) L10001
-
Force analysis of jamming with disks of different sizes in a two-dimensional hopper
Anthony Longjas et al J. Stat. Mech. (2009) P05006
-
A new type of critical behaviour in random matrix models
R Flume and A Klitz J. Stat. Mech. (2008) N10001
-
Extreme value problems in random matrix theory and other disordered systems
Giulio Biroli et al J. Stat. Mech. (2007) P07019
-
Dyck paths, Motzkin paths and traffic jams
R A Blythe et al J. Stat. Mech. (2004) P10007
-
A role for helical intermediates in amyloid formation by natively unfolded polypeptides?
Andisheh Abedini and Daniel P Raleigh 2009 Phys. Biol. 6 015005
-
Detecting translations of the same text and data with common source
Kostadin Koroutchev and Manuel Cebrián J. Stat. Mech. (2006) P10009
-
The transfer matrix of a superintegrable chiral Potts model as the Q operator of root-of-unity XXZ chain with cyclic representation of
Shi-shyr Roan J. Stat. Mech. (2007) P09021
-
Molecular spiders in one dimension
Tibor Antal et al J. Stat. Mech. (2007) P08027
Users also read
What's this?Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Universality of Wigner random matrices: a survey of recent results