| Upon successful completion of the course, students are able to demonstrate a comprehensive understanding of simulation methods in physics (listed below), and can apply these methods. They are able to write computer programs to solve many-body problems from classical and, optionally, quantum physics.
This exercise is building on topics introduced in the lecture and exercise Computational Physics I. It is methodologically complemented by the lecture Computational Physics II.
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Upon completing the course, students will possess the following skills. They are able to
- understand mathematical derivations and formulations of numerical methods required for computer simulations (k2);
- apply these methods by writing computer code (k3);
- assess the correctness of simulation results obtained with their code, and identify possible errors in their implementation or choice of method (k4/k5);
- analyze and quantify the accuracy of numerical results (k4/k5);
- determine the best choice of algorithms for advanced numerical problems in many-body simulations (k5).
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During the course, students will acquire knowledge about numerical techniques concerning:
- symplectic integrators for ordinary differential equations;
- force fields and their efficient calculation;
- molecular dynamics simulations in different ensembles;
- diffusion, rare events (optional), autocorrelations and the fluctuation dissipation theorem;
- Markov processes and the Metropolis algorithm;
- Monte Carlo simulation methods for classical statistical mechanics in different ensembles;
- quantum Monte Carlo methods for ground state and finite temperature simulations (optional).
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