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Microlocal Analysis, Sharp Spectral Asymptotics and Applications V: Applications to Quantum Theory and Miscellaneous Problems

✍ Scribed by Victor Ivrii

Publisher
Springer International Publishing
Year
2019
Tongue
English
Leaves
761
Edition
1st ed. 2019
Category
Library
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✦ Synopsis

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in β€œsmall” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic SchrΓΆdinger operator, miscellaneous problems, and multiparticle quantum theory.

In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.


✦ Table of Contents

Front Matter ....Pages I-XXIV
Front Matter ....Pages 1-1
No Magnetic Field Case (Victor Ivrii)....Pages 2-67
The Case of External Magnetic Field (Victor Ivrii)....Pages 68-207
The Case of Self-Generated Magnetic Field (Victor Ivrii)....Pages 208-283
The Case of Combined Magnetic Field (Victor Ivrii)....Pages 284-394
Back Matter ....Pages 395-466
Front Matter ....Pages 467-467
Spectral Asymptotics for the Semiclassical Dirichlet to Neumann Operator (Andrew Hassell, Victor Ivrii)....Pages 468-494
Spectral Asymptotics for Fractional Laplacians (Victor Ivrii)....Pages 495-512
Spectral Asymptotics for Dirichlet to Neumann Operator in the Domains with Edges (Victor Ivrii)....Pages 513-539
Asymptotics of the Ground State Energy in the Relativistic Settings (Victor Ivrii)....Pages 540-558
Asymptotics of the ground state energy in the relativistic settings and with self-generated magnetic field (Andrew Hassell, Victor Ivrii)....Pages 559-581
Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators (Victor Ivrii)....Pages 583-606
Complete Differentiable Semiclassical Spectral Asymptotics (Victor Ivrii)....Pages 607-618
Bethe-Sommerfeld Conjecture in Semiclassical Settings (Victor Ivrii)....Pages 619-639
100 years of Weyl’s Law (Victor Ivrii)....Pages 641-729
Back Matter ....Pages 730-739

✦ Subjects

Mathematics; Analysis; Mathematical Physics

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