Parallel axis theorem for free-space electron wavefunctions

We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular momentum of the cyclotron orbit of the wavefunction, and a diamagnetic angular momentum. The cyclotron and diamagnetic angular momenta are found to be separable according to the parallel axis theorem. This means that rotations can occur with respect to two or more axes simultaneously, which can be observed with superpositions of vortex states

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying ``diamagnetic'' angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields

The diamagnetic angular momentum of an electron

Diamagnetism is the magnetism exhibited by all materials, even those not normally considered magnetic, in the presence of an applied magnetic field. On a microscopic level, it is associated with the angular momentum acquired by individual electrons in the magnetic field. Recently discovered electron vortices, meanwhile, possess orbital angular momentum even in field-free space. In this thesis, I consider the angular momentum of an arbitrary electron wavefunction in a uniform magnetic field. I show that the kinetic orbital angular momentum of the electron can be represented as a sum of three components: the canonical angular momentum associated with a vortex, the angular momentum associated with a cyclotron orbit of the wavefunction as a whole, and a “diamagnetic” angular momentum associated with an internal rotation of the wavefunction that is induced by the magnetic field. I show that the diamagnetic angular momentum depends on the moment of inertia of the electron’s probability distribution, which for free electrons has interesting consequences. Whereas diamagnetism in materials is normally very small compared to the effects of intrinsic magnetic moments, a free electron – for example, in an electron microscope – can have a probability distribution with a much larger average radius. This means that the diamagnetic component can be the dominant contribution to the electron’s angular momentum. On the other hand, the diamagnetic angular momentum may instead be of a similar magnitude to the canonical and/or cyclotron components, in which cases the current density strongly depends on the relative magnitudes and directions of these components. Further, diffraction and interference of the electron’s wave function lead to interesting dynamical effects. I demonstrate that the kinetic angular momentum of the electron can vary with time, which seems at first sight to violate angular momentum conservation. The diamagnetic angular momentum also gives rise to a “Faraday effect” for electrons, analogous to the rotation of the polarization of light in a magnetic field. All of this behaviour is a surprising departure from the simple cyclotron orbit predicted by classical theory

Is the Angular Momentum of an Electron Conserved in a Uniform Magnetic Field?

We show that an electron moving in a uniform magnetic field possesses a time-varying ``diamagnetic'' angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields

Analysis of lectin binding to glycolipid complexes using combinatorial glycoarrays

Glycolipids are major components of the plasma membrane, interacting with themselves, other lipids, and proteins to form an array of heterogeneous domains with diverse biological properties. Considerable effort has been focused on identifying protein binding partners for glycolipids and the glycan specificity for these interactions, largely achieved through assessing interactions between proteins and homogenous, single species glycolipid preparations. This approach risks overlooking both the enhancing and attenuating roles of heterogeneous glycolipid complexes in modulating lectin binding. Here we report a simple method for assessing lectin-glycolipid interactions. An automatic thin-layer chromatography sampler is employed to create easily reproducible arrays of glycolipids and their heterodimeric complexes immobilized on a synthetic polyvinyl-difluoride membrane. This array can then be probed with much smaller quantities of reagents than would be required using existing techniques such as ELISA and thin-layer chromatography with immuno-overlay. Using this protocol, we have established that the binding of bacterial toxins, lectins, and antibodies can each be attenuated, enhanced, or unaffected in the presence of glycolipid complexes, as compared with individual, isolated glycolipids. These findings underpin the wide-ranging influence and importance of glycolipid-glycolipid cis interactions when the nature of protein-carbohydrate recognition events is being assessed