TY - JOUR

T1 - Lévy meets Boltzmann

T2 - International Workshop on Frontiers in the Physics of Complex Systems

AU - Metzler, Ralf

AU - Klafter, Joseph

N1 - Funding Information:
RM thanks the Chemical Physics Department in the School of Chemistry, Tel Aviv University for the hospitality and the possibility to carry out this work. RM also acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) within the Emmy Noether programme.

PY - 2001/12/15

Y1 - 2001/12/15

N2 - We study normal and anomalous diffusion processes with initial conditions of the broad Lévy type, i.e., with such initial conditions which, per se, exhibit a diverging variance. In the force-free case, the behaviour of the associated probability density function features distinct shoulders which can be related to the probability current flowing away from the origin. In the presence of an external potential which eventually leads to the emergence of a non-trivial, normalisable equilibrium probability density function, the initially diverging variance becomes finite. In particular, the effects of strange initial conditions for the harmonic Ornstein-Uhlenbeck potential are explored to some detail. Methods to quantify the dynamics related to such kinds of processes are investigated.

AB - We study normal and anomalous diffusion processes with initial conditions of the broad Lévy type, i.e., with such initial conditions which, per se, exhibit a diverging variance. In the force-free case, the behaviour of the associated probability density function features distinct shoulders which can be related to the probability current flowing away from the origin. In the presence of an external potential which eventually leads to the emergence of a non-trivial, normalisable equilibrium probability density function, the initially diverging variance becomes finite. In particular, the effects of strange initial conditions for the harmonic Ornstein-Uhlenbeck potential are explored to some detail. Methods to quantify the dynamics related to such kinds of processes are investigated.

KW - Fokker-Planck equation

KW - Fractional Fokker-Planck equation

KW - Gibbs-Boltzmann equillibrium

KW - Stable initial conditions

UR - http://www.scopus.com/inward/record.url?scp=0035894707&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(01)00472-1

DO - 10.1016/S0378-4371(01)00472-1

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AN - SCOPUS:0035894707

SN - 0378-4371

VL - 302

SP - 290

EP - 296

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-4

Y2 - 25 March 2001 through 28 March 2001

ER -