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In order to gain a better understanding of the Drude model I'm going guide you through a

numerical experiment. For this problem you are going to need a computer and a software of your

choice (Matlab, Mathematica, Octave, Excel, C, Python, Candy Crush, or whatever you like).

Whatever software you choose you need to be able to do the following elementary operations:

1) Generate a list of random numbers

2) Add lists of numbers element by element

3) Perform comparisons (i.e. "If" commands)

4) Perform iterations (i.e. "For", "While", etc. commands)

5) Plot your results

Description of the problem

Let us try to monitor the behavior of a particle of mass m=1 moving under the action of a constant

force F=1 and undergoing collisions with an average collision time r=1. We are going to monitor

the velocity of the particle over an extended interval of time T>T. We are going to update the

particle's velocity at intervals of dt<

intervals, so that T=10. The procedure that mimics the Drude model is the following:

1) Setup the initial velocity at time t=0 by generating a random real number between -1 and

+1, i.e. if you were using Mathematica something of this sort: v[0]=RandomReal[{-1,1}].

2) Determine whether or not the particle undergoes a collision in the next time interval dt.

You know that according to the Drude model the probability of collision during a small

time interval dt is Pe=dt/t. One way to implement this condition is to generate a random

real number X between 0 and 1, and say that a collision occurred if X

Fig: 1