Momento oculto em sistemas quânticos e sua relação com o momento da luz na matéria

Abstract

In a recent paper, Mansuripur presented an apparent paradox that seemed to imply that the Lorentz force is incompatible with special relativity and momentum conservation. However, it was shown that this paradox disappears if one takes into account the hidden momentum of the system. Therefore, the validity of the Lorentz force is conditioned to the existence of hiddenmomentum. The hidden momentum is a relativistic effect that appears, for example, when a magnetic dipole is subject to an electric field. This effect may cause the dipole to have a nonzero linear momentum even if it is not moving. Until recently there were only classic models to hidden momentum and therefore it was not known whether the Lorentz force would be also valid in quantum systems. In the first part of this thesis, with the aim of checking the validity of the Lorentz force in quantum systems, we consider a hydrogen atom withmagnetic dipole moment due to the orbital state of the electron subjected to an external electric field.We calculate the expected value of the relativistic momentum of the electron by using perturbation theory, showing that it is compatible with the hidden momentum, and therefore with the validity of the Lorentz force on quantum systems. There is a famous dilemma, known as Abraham-Minkowski debate, aboutwhat is the expression for themomentum density of an electromagneticwave when it pene- trates into amaterialmedium. There are several different approaches to the treatment of this problem, the most famous being the Abraham and Minkowski ones. In the second part of this thesis, we show the implications of the concept of hidden momentum for the Abraham-Minkowski debate. In particular, we show that the models for the electric and magnetic dipoles of the medium are associated with the presence or absence of hiddenmomentumin the system.We considermodels inwhich the dipoles can be due to electric ormagnetic charges aswell as electric ormagnetic currents.We showhowthe dipolemodels affect the expressions that should be used for the electro- magnetic part of the wave momentum in the medium, with eachmodel corresponding toadifferentexpression.