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Biography
Mihail Nedjalkov, born in Sofia, Bulgaria received the master's degree in semiconductor physics at the Sofia University "Kl. Ohridski", a PhD degree (1990), habilitation (2001) and D.Sc. degree (2011) at the Bulgarian Academy of Sciences (BAS). He is Associate Professor with the Institute of Information and Communication Technologies, BAS, but held visiting research positions at the University of Modena (1994), University of Frankfurt (1998), Arizona State University (2004) and mainly at the Institute for Microelectronics, Technische Universität Wien, supported by the following European and Austrian projects: EC Project NANOTCAD (2000-03), Österreichische Forschungsgemeinschaft MOEL 239 and 173 (2007-08), FWF (Austrian Science Fund) P-13333-TEC (1998-99), START (2005-06), P-21685 (2009-2014) and the current EC-FP7 Project SUPERTHEME. He has served as a lecturer at the 2004 International School of Physics 'Enrico Fermi', Varenna, Italy, and has over 150 publications. His research interests include physics and modeling of classical and quantum carrier transport in semiconductor materials, devices and nanostructures, collective phenomena, theory and application of stochastic methods.
The Aharanov-Bohm Effect from a Phase Space Perspective
We consider a charged particle interacting with an electromagnetic medium. The classical motion of a particle follows a trajectory, which, according to Newton's second law of dynamics, is governed by forces represented by the Lorentz force and comprised of the joint action of electric and magnetic fields. These vector fields are uniquely described by the Maxwell equations, where the six components of the two vector fields appear as arguments. This description may be facilitated by the introduction of electromagnetic potentials. These are the scalar and vector potentials, whose first derivatives determine the vector field components and in this way reduce the number of the unknown arguments from six to four. From this point of view the potentials are merely a mathematical construct to simplify calculations, and have a rather auxiliary physical interpretation.
Quantum mechanics is based on potentials, meaning that the quantum state depends not only on the field part but on all terms beyond the first derivative in the series expansion of a given potential. Such a dependence causes an experimentally observed phenomena, known as the Aharonov-Bohm effect. The physical aspect of this effect can be shortly addressed as a change of the particle state, despite the fact that the latter evolves in a region with no electric and magnetic forces. In particular, if two solutions of the Schrödinger equation with zero and constant potential are compared, in the latter case the wave function acquires some additional phase. In an interference experiment this shift of the phase gives rise to a change of the intensity pattern, despite no fields directly acting on the particle.
This effect is analyzed from a phase space perspective with the help of the Wigner formulation of quantum mechanics. Simulation results show that the effect is revealed by the dependence of the interference part of the entangled electron state on the potential value. It is discussed how the destruction of this interference part recovers the classical behavior.
