The “Wandering Photon”
An Animation Found on the Internet!
Animated Illustration of the Random Walk Problem
The “Wandering Photon”
Photon
• A photon walks straight for a random distance.
• It stops random,lywith probability g . It turns
in a random direction with probability (1-g).
A One-Dimensional
“Wandering Photon”
x
After walking to the right for a random distance x, it stops
with probability g. After each stop, there is a probability
(1-g)/2 for it to continue to the right & a probability
(1-g)/2 for it to continue to the left.
x
x
x
x
x
x
What is the Probability P of
a photon being absorbed at x?
x
pdf of the length of the first step
1/h = average step length γ = absorption probability
P(photon absorbed at x) = f (|x|,g,η)

gh
2
e
 gh x
x
pdf of the length of the first step
1/h = average step length γ = absorption probability
“The Sleepy Photon” or
“The Sleepy Drunk”
in higher dimensions
After walking a random distance r, it stops with
probability g. Then, with probability (1-g ), it picks a
random direction to continue walking.
“The Sleepy Photon” or
“The Sleepy Drunk”
in higher dimensions
r
P(absorbed at r) = f (r,g,h)