By Yuri Kondratiev, Yuri Kozitsky, and Michael Rockner Sergio Albeverio
Quantum statistical mechanics performs an enormous position in lots of fields corresponding to thermodynamics, plasma physics, solid-state physics, and the research of stellar constitution. whereas the idea of quantum harmonic oscillators is comparatively basic, the case of anharmonic oscillators, a mathematical version of a localized quantum particle, is extra complicated and demanding. furthermore, endless structures of interacting quantum anharmonic oscillators own attention-grabbing ordering houses with admire to quantum stabilization. This ebook provides a rigorous method of the statistical mechanics of such platforms, particularly with appreciate to their activities on a crystal lattice. The textual content is addressed to either mathematicians and physicists, specifically people who are concerned about the rigorous mathematical history in their effects and the type of difficulties that come up in quantum statistical mechanics. The reader will locate the following a concise choice of proof, recommendations, and instruments suitable for the appliance of direction integrals and different equipment in response to degree and integration idea to difficulties of quantum physics, particularly the newest leads to the mathematical conception of quantum anharmonic crystals. The equipment constructed within the ebook also are acceptable to different difficulties concerning infinitely many variables, for instance, in biology and economics.
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