14 research outputs found

    Nonadiabatic extension of the Heisenberg model

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    The localized states within the Heisenberg model of magnetism should be represented by best localized Wannier functions forming a unitary transformation of the Bloch functions of the narrowest partly filled energy bands in the metals. However, as a consequence of degeneracies between the energy bands near the Fermi level, in any metal these Wannier functions cannot be chosen symmetry-adapted to the complete paramagnetic group M^P. Therefore, it is proposed to use Wannier functions with the reduced symmetry of a magnetic subgroup M of M^P [case (a)] or spin dependent Wannier functions [case (b)]. The original Heisenberg model is reinterpreted in order to understand the pronounced symmetry of these Wannier functions. While the original model assumes that there is exactly one electron at each atom, the extended model postulates that in narrow bands there are as many as possible atoms occupied by exactly one electron. However, this state with the highest possible atomiclike character cannot be described within the adiabatic (or Born-Oppenheimer) approximation because in the (true) nonadiabatic system the electrons move on localized orbitals that are still symmetric on the average of time, but not at any moment. The nonadiabatic states have the same symmetry as the adiabatic states and determine the commutation properties of the nonadiabatic Hamiltonian H^n. The nonadiabatic Heisenberg model is a purely group- theoretical model which interprets the commutation properties of H^n that are explicitly given in this paper for the two important cases (a) and (b). There is evidence that the occurrence of these two types of Wannier functions in the band structure of a metal is connected with the occurrence of magnetism and superconductivity, respectively

    The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

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    This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics
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