TY  - JOUR
A1  - Xu, Pengbo
A1  - Zhou, Tian
A1  - Metzler, Ralf
A1  - Deng, Weihua
T1  - Stochastic harmonic trapping of a Lévy walk
BT  - transport and first-passage dynamics under soft resetting strategies
JF  - New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
N2  - We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
KW  - diffusion
KW  - anomalous diffusion
KW  - stochastic resetting
KW  - Levy walks
Y1  - 2022
U6  - https://doi.org/10.1088/1367-2630/ac5282
SN  - 1367-2630
VL  - 24
IS  - 3
SP  - 1
EP  - 28
PB  - Deutsche Physikalische Gesellschaft
CY  - Bad Honnef
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
A1  - Domazetoski, Viktor
A1  - Kocarev, Ljupco
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei
T1  - Heterogeneous diffusion with stochastic resetting
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study a heterogeneous diffusion process (HDP) with position-dependent diffusion coefficient and Poissonian stochastic resetting. 

We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. 
We also analyse the transition to the non-equilibrium steady state by finding the large deviation function. 

We found that similarly to the case of the normal diffusion process where the diffusion length grows like t (1/2) while the length scale xi(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the HDP with diffusion length increasing like t ( p/2) the length scale xi(t) grows like t ( p ). 

The obtained results are verified by numerical solutions of the corresponding Langevin equation.
KW  - heterogeneous diffusion
KW  - Fokker-Planck equation
KW  - Langevin equation
KW  - stochastic resetting
KW  - nonequilibrium stationary state
KW  - large deviation function
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac491c
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 7
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -