Consider an one-dimensional lattice with lattice constant a. An atom transits from a site to a nearest neighbour site every τ seconds. The probability of transiting to the right and left are p and q = (1 − p) respectively. Calculate the average position of the atom at time t = Nτ , where N >> 1.

Consider an one-dimensional lattice with lattice constant a. An atom transits from a site to a nearest neighbour site every τ seconds. The probability of transiting to the right and left are p and q = (1 − p) respectively. Calculate the average position of the atom at time t = Nτ , where N >> 1.

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Consider an one-dimensional lattice with lattice constant a. An atom transits from a site to
a nearest neighbour site every τ seconds. The probability of transiting to the right and left are p and
q = (1 − p) respectively. Calculate the average position of the atom at time t = Nτ , where N >> 1.
Calculate the mean square value < (x− < x >)
2 > and the relative fluctuation at time t.

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