TY - JOUR
T1 - Random walks on random lattices with traps
AU - Halpern, V.
PY - 1983/2
Y1 - 1983/2
N2 - A critical examination is presented of the continuous time random walk (CTRW) approximation and of frequency-dependent effective transition rate methods for calculating the configurational average of the Laplace transform of the probability Ps, t|0) that a particle performing a random walk will be at site s time t after it reached the site s0. Some exact results are derived for the form of P(s, t|s0) at long times, and these indicate that the effective transition rate methods are the better approximation for systems with symmetric effective hopping rates, while the CTRW approximation is better for systems containing traps, i.e., states that are much easier to enter than to leave. The implications of these results for calculations of transient currents and of the ac conductivity for amorphous semiconductors are discussed.
AB - A critical examination is presented of the continuous time random walk (CTRW) approximation and of frequency-dependent effective transition rate methods for calculating the configurational average of the Laplace transform of the probability Ps, t|0) that a particle performing a random walk will be at site s time t after it reached the site s0. Some exact results are derived for the form of P(s, t|s0) at long times, and these indicate that the effective transition rate methods are the better approximation for systems with symmetric effective hopping rates, while the CTRW approximation is better for systems containing traps, i.e., states that are much easier to enter than to leave. The implications of these results for calculations of transient currents and of the ac conductivity for amorphous semiconductors are discussed.
KW - Random walk
KW - ac conductivity
KW - amorphous semiconductors
KW - transient currents
UR - http://www.scopus.com/inward/record.url?scp=34250151529&partnerID=8YFLogxK
U2 - 10.1007/bf01012311
DO - 10.1007/bf01012311
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AN - SCOPUS:34250151529
SN - 0022-4715
VL - 30
SP - 373
EP - 381
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -