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

Description

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 “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger 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. 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