8

Question 1

Monte Carlo

Answer 1

Question 2

Monte Carlo

The trial changes in configuration are positive or negative shifts through ∆x 0 in dimensionless displacement. Some attempted shifts are guaranteed to be accepted: which ones?

Answer 2

Trial moves that are automatically accepted are those that reduce the energy

Question 3

Monte Carlo

How would you implement acceptance?

Answer 3

Question 4

Monte Carlo

Answer 4

Question 5

Liouville’s equation

Answer 5

Question 6

Hamilton’s equations

Answer 6

Question 7

Derive Liouville’s eq

Answer 7

Liouville’s theorem of phase space conservation tells us that dΓ and dΓ0 have equal size (in the sense of phase space volume).Given a total probability that the system takes one of the phase space points in dΓ at time t, then the same probability must be attached to occupancy of one of the points in dΓ(0 )at t + dt, and so we conclude that the density of probability on the phase space at Γ(t) and Γ(t+dt) must be the same.

Question 8

Answer 8

Question 9

Kramers-Moyal coefficients

Answer 9

Question 10

Kramers-Moyal equation

Answer 10

Question 11

Fokker-Planck eq

Answer 11

Question 12

Wiener process pdf

Answer 12