TY  - JOUR
A1  - Xu, Pengbo
A1  - Metzler, Ralf
A1  - Wang, Wanli
T1  - Infinite density and relaxation for Levy walks in an external potential
T2  - Physical review
N2  - Levy walks are continuous-time random-walk processes with a spatiotemporal coupling of jump lengths and waiting times. We here apply the Hermite polynomial method to study the behavior of LWs with power-law walking time density for four different cases. First we show that the known result for the infinite density of an unconfined, unbiased LW is consistently recovered. We then derive the asymptotic behavior of the probability density function (PDF) for LWs in a constant force field, and we obtain the corresponding qth-order moments. In a harmonic external potential we derive the relaxation dynamic of the LW. For the case of a Poissonian walking time an exponential relaxation behavior is shown to emerge. Conversely, a power-law decay is obtained when the mean walking time diverges. Finally, we consider the case of an unconfined, unbiased LW with decaying speed v(r ) = v0/./r. When the mean walking time is finite, a universal Gaussian law for the position-PDF of the walker is obtained explicitly.
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/62573
SN  - 2470-0045
SN  - 2470-0053
VL  - 105
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -