Quantum theory and applications

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Quantum mechanics governs essentially all phenomena at microscopic scales and below. I intend to examine several problems in quantum mechanics and its more sophisticated relative, quantum field theory.Two of these problems are in the context of solitons, which are extended solutions of classical field theory which resemble particles in their behaviour. While not intrinsically quantum mechanical, these objects exist in quantum field theory as well.Another research project pertains to the Josephson effect in superconductivity from a field theory perspective, as well as a generalization of this effect to situations where the underlying symmetry is of a type known as non-abelian.An important property of the strong interaction which holds nuclei together is confinement, the fact that certain fundamental particles (quarks and gluons) cannot be isolated from one another. This property is as widely accepted as it is difficult to actually prove. Two projects on which I am working study toy models which may or may not have this property; what is learned from the toy models will hopefully shed light on more realistic models.Anoher research effort represents a bit of a change of direction for me, towards quantum information, a new and vigourous field of research. One specific problem I am investigating is the conditions of validity of the so-called adiabatic theorem in quantum mechanics. This theorem has been known since the early days of quantum mechanics, yet the exact conditions under which it is valid have come under scrutiny lately. Secondly, I am studying the simulation of generalized quantum measurements on an entangled quantum system using classical communication, which is a subject of great interest in quantum information and quantum communication.