A particle hops randomly from a site to its nearest neighbour in each step on a square lattice of unit lattice constant. The probability of hopping to the positive x-direction is 0.3, to the negative x-direction is 0.2, to the positive y-direction is 0.2 and to the negative y-direction is 0.3. If a particle starts from the origin, its mean position after N steps is

Question

Question

Answer 1

Concept:

The hopping probability is exponential in the height only of the (free) energy barrier between sites.

Calculation:

<r_i> ∑ p_ir_i

= 0.3i - 0.2i + 0.2j - 0.3j

= 0.1i - 0.1j

For N steps, = $\frac{N}{10}$ [i - j]

The correct answer is option (2).

Download Solution PDF