TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Thapa, Samudrajit
A1  - Mardoukhi, Yousof
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Time averages and their statistical variation for the Ornstein-Uhlenbeck process
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.
Y1  - 2018
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/52153
SN  - 2470-0045
SN  - 2470-0053
VL  - 98
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  -