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Understanding Monte Carlo Algorithm and its application to a Bose-Einstein System
Pragati Ashdhir, Yash Saxena, Adesh Kushwaha and Karun Gadge
Hindu College, University of Delhi
In this paper we study the Monte Carlo Al- gorithm using two different sampling methods, namely, Direct sampling and Markov chain sam- pling. In the Markov chain sampling method, Metropolis algorithm is used. The paper explains the Monte Carlo algorithm and the different sampling approaches in a simplified manner. In connection with this we explore the theory of evaluation of integrals and Hamiltonians. To further clarify the tools, a problem of Boson Gas under a harmonic potential trap is chosen and solved using the Monte Carlo Method. The results obtained using different approaches are compared and presented in the form of plots. The aim of this exercise is to efficiently deliver the concept of Monte Carlo method to the graduate and post-graduate physics students and aid in enhancing their computational skills.
Monte Carlo, Variational Principle, Direct Sampling, Markov Chain