Monte-Carlo simulation Coulomb potential scattering

[wronski77]

Dear all,

I just started learning about the Monte-Carlo methods of simulating particle interactions. I would like to ask a question about simulating potential scattering. In particular I think that the simulating scattering by Coulomb potential, and writing a corresponding MC test program might be a good start to understand the ideas.

Is it possible to use Markov chains in order to simulate the above described problem? Let’s say define the potential and use the configuration part of the partition function in order to decide the motion of the particle.

The other possibility I can think of is to write down the differential equation, based on the interaction Lagrangian. After this is done one can use Monte Carlo in order to simulate the differential equation. We result in an ODE, which is easy to simulate with Monte Carlo, given some boundary conditions.

I would be very grateful if someone can give me ideas how simulate the scattering form Coulomb potential.

Thank you in advance

Wronski

 

[eljose79]

Dear Wronski,

Thank you for your interest in Monte-Carlo methods and their application to simulating particle interactions. To answer your question, yes, it is possible to use Markov chains to simulate the scattering by Coulomb potential. In fact, Markov chain Monte Carlo (MCMC) methods have been widely used in simulating a variety of physical systems, including particle interactions.

One approach to simulating the scattering by Coulomb potential using MCMC is to define the potential and use the Metropolis-Hastings algorithm to sample the positions and velocities of the particles. This algorithm uses the configuration part of the partition function to determine the acceptance or rejection of the proposed configurations, effectively simulating the motion of the particles in the Coulomb potential.

Another approach is to use the differential equation method you mentioned. This involves writing down the differential equation based on the interaction Lagrangian and then using MCMC to simulate the equation. This approach may be more computationally intensive, but it allows for more detailed simulations and the inclusion of boundary conditions.

I would also recommend considering other Monte-Carlo methods, such as importance sampling or rejection sampling, which may be more efficient for simulating specific scenarios.

I hope this helps guide you in your exploration of simulating the scattering by Coulomb potential using Monte-Carlo methods. Best of luck in your research!