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Exact Solutions of Few First Passage Problems in Linear Correlated Walks. Applications to the Electron Trapping in a Semiconductor
Author(s) -
Godoy S.,
Fujita S.
Publication year - 1988
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221470224
Subject(s) - laplace transform , electron , random walk , semiconductor , trapping , lattice (music) , mathematics , transformation (genetics) , linear correlation , statistical physics , fourier transform , physics , combinatorics , quantum mechanics , mathematical analysis , chemistry , statistics , acoustics , ecology , biochemistry , gene , biology
The average number of steps, 〈 N 〉, in which a walker gets trapped at the origin when he starts at one of L − 1 non‐trap sites on a looping linear lattice of L points, is calculated for an arbitrary correlation. It is given by 〈 N 〉 = ( L /6(1 + δ)) [(1 − δ) L + 1 + 5δ], where δ = α − β is the degree of correlation with α and β respresenting step probabilities for forward and direction‐changing motion, respectively. This result and others are obtained by solving basic difference equations for linear correlated walks with the aid of Fourier‐Laplace transformation techniques. Potential applications of the theory to trappings of electrons in a semiconductor and others are discussed.