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- Random Operators and Stochastic Equations
- NSF Award Search: Award# - Disorder Effects on Quantum Spectra and Dynamics
The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.
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The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results.
The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.
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Bloggat om Random Operators. Such exponential increase is found not only on trees but also in the configuration spaces of interacting particles, and work is in progress now on the possible ramifications of this observation for many particle systems.
Rounding of Quantum First Order Transitions in low dimensional systems The PI has also been engaged in the study on the effects of disorder on 1st order phase transitions in homogeneous quantum systems. The main result derived jointly with J.
Lebowitz and R. Once again in this area, the mathematical result have clarified issues of physics while these have still been the subject of ongoing debates. Work continues currently on the interesting nature of the phase transition which may remain there at weak disorder jointly with J.
Hanson, a graduate student. In terms of mathematics, the work has involved the combination of functional analysis, operator theory, probability, and techniques which have originated in mathematical physics.
Random Operators and Stochastic Equations
Typically, significant results were published in leading mathematics journals or leading journals dedicated to mathematical physics, and when that was deemed appropriate an abbreviated summary of the results was presented in parallel to the physics community through venues such as Phys.
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NSF Award Search: Award# - Disorder Effects on Quantum Spectra and Dynamics
Recently added grants:. Source Duke Math. Zentralblatt MATH identifier A characterization of the Anderson metal-insulator transport transition. Duke Math.
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