@article{JeonChechkinMetzler2014, author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion}, series = {Physical chemistry, chemical physics : PCCP}, volume = {30}, journal = {Physical chemistry, chemical physics : PCCP}, number = {16}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, doi = {10.1039/C4CP02019G}, pages = {15811 -- 15817}, year = {2014}, abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.}, language = {en} } @misc{JeonChechkinMetzler2014, author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76302}, pages = {15811 -- 15817}, year = {2014}, abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.}, language = {en} }