who can help me with my homework in calculation of the mean potencial of non harmonic oscillations with hybrid monte carlo? I am looking for ideas or guided chat. what about integral and exponential autocorrelated time?

$$P(x_1,x_2,...,x_N) \sim e^{-\beta V(x_1,x_2,...,x_N)}$$

$$V(x_1,x_2,...,x_N)=\sum^N_{i=1}{1 \over 2}\lbrace(x_{i+1}-x_i)^2+v(x_i)+v(x_{i+1})\rbrace$$

$$v(x)={x^2 \over 2}+{\lambda \over 4}(x^2-\delta)^2 , x \in {\bf R}$$

Tex-mode is done with putting the math code between [ math] and [ /math] tags not Dollars leading to

[math]P(x_1,x_2,...,x_N) = e^{-\beta V(x_1,x_2,...,x_N)} / Z[/math],

[math]V(x_1,x_2,...,x_N)=\sum^N_{i=1}{1 \over 2}\lbrace(x_{i+1}-x_i)^2+v(x_i)+v(x_{i+1})\rbrace [/math],

[math]v(x)={x^2 \over 2}+{\lambda \over 4}(x^2-\delta)^2 , x \in {\bf R}[/math].

 

For the question: I only have some basic knowledge about Monte-Carlo methods. I do not know what "hybrid Monte-Carlo" is. What exactly is your problem? Have you written a Monte-Carlo and it does not work? Does it work but you want to use this "hybrid Monte-Carlo" technique? What is or would be your algorithm? I do not believe that statements about correlation time can be made independently of a concrete algorithm (not that I think I could say much about them if you had presented one, but your post/question seems incomplete to me).

Atheist, you have misunderstand me. I can not ask and expect in this forum

a solution to my problem. I expect and thank you for statements like "I do not believe that statements about correlation time can be made independently of a concrete algorithm " which are correct. My post/question is complete. Words like "non harmonic quantum oscillations" are additions

for fun, important is only the potential. I don't have written any Monte-Carlo and I have only some ideas for the algorithm of Hybrid Monte Carlo.

Hybrid Monte Carlo is a method for the numerical simulation of lattice field theory. A hybrid algorithm is used to guide a Monte Carlo simulation. There are no discretization errors even for large step size. The method is especially efficient for systems such as quantum chromodynamics which contain fermionic degrees of freedom. If you want I can email you a paper "S. Duane, A. D. Kennedy, B. Pendleton, and D. Roweth, Hybrid Monte Carlo. Physics Letters B, 195(2):216–222, 1987."

Please don't ask me anything because I don't know. Last term I had "computational physics" and my proffesor gave us the course in a very very strange way, he often says " like engineers learn and do things".