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Posted: Nov 26, 2014
Series of lectures on Wigner Monte Carlo methods
(Nanowerk News) Very recently, the Bulgarian Academy of Sciences has provided a series of short lectures on YouTube on the Wigner formulation of quantum mechanics and its related Monte Carlo method based on signed particles. The lectures are given by Dr. Jean Michel Sellier who is the leading scientist in this particular field. With these lectures, Dr. Sellier hopes to spread the word around the novel methods which have been created in the field of single- and many-body quantum problems.
The five lectures discuss different aspects and usages of this formulation of quantum mechanics:
In the first lecture, Dr. Sellier discusses the Wigner formulation of Quantum Mechanics which is based on the concept of quasi-distributions defined over the phase-space. This is an interesting seminar which shows the equivalence of the Wigner and the Schrodinger formulations.
In the second lecture, the Wigner Monte Carlo method applied to single-body quantum systems is introduced. Mathematical details are given on how to implement this method along with refernces for further details and reading.
In the third lecture, Dr. Sellier discusses the Wigner Monte Carlo method in the framework of density functional theory (DFT). This is the first time the Wigner formalism is extended to quantum many-body problems. Validations on benchmark tests are presented on boron, lithium and hydrogen atoms and molecules.
In the fourth lecture, the ab initio Wigner Monte Carlo method for the simulation of strongly correlated systems is discussed. This method is capable of time-dependent ab-initio calculations without introducing approximations to the many-body problem. This is the first Monte Carlo method able to simulate the time-dependent many-body Wigner equation.
In the fifth lecture, Dr. Sellier discusses systems of indistinguishable Fermions in the Wigner formulation of quantum mechanics. In particular, it is shown that the Pauli exclusion principle is naturally embedded in the Wigner formalism.