M Constantin et al J. Stat. Mech. (2007) P07011 doi:10.1088/1742-5468/2007/07/P07011
M Constantin1, C Dasgupta2, S Das Sarma3, D B Dougherty4 and E D Williams5
Show affiliationsPart of Focus on Dynamics of Non-Equilibrium Systems
Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations, are considered. Results of experiments in which dynamical scanning tunnelling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
68.37.Ef Scanning tunneling microscopy (including chemistry induced with STM)
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
60A10 Probabilistic measure theory (For ergodic theory, see 28Dxx and 60Fxx)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
Issue 07 (July 2007)
Received 24 February 2007, accepted for publication 23 April 2007
Published 6 July 2007
M Constantin et al J. Stat. Mech. (2007) P07011
Niklas Beisert et al J. Stat. Mech. (2007) P01021
D Challet et al J. Stat. Mech. (2008) L04004
Su-Chan Park and Joachim Krug J. Stat. Mech. (2008) P04014
Charlotte Gils et al J. Stat. Mech. (2007) P09011
Vivien Lecomte and Julien Tailleur J. Stat. Mech. (2007) P03004
Doogie Oh et al 2010 J. Phys.: Condens. Matter 22 084001
P W Messer et al J. Stat. Mech. (2005) P10004
Helmut G Katzgraber et al J. Stat. Mech. (2006) P03018
Iwan Jensen J. Stat. Mech. (2009) P02065