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Author: Mouez Dimassi
Publisher: Cambridge University Press
Published: 1999-09-16
Total Pages: 243
ISBN-13: 0521665442
DOWNLOAD EBOOKThis book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Mouez Dimassi
Publisher:
Published: 2014-05-14
Total Pages: 241
ISBN-13: 9781107362796
DOWNLOAD EBOOKThis book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Victor Ivrii
Publisher: Springer Nature
Published: 2019-09-12
Total Pages: 938
ISBN-13: 3030305570
DOWNLOAD EBOOKThe 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 general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.
Author: Johannes Sjöstrand
Publisher: Springer
Published: 2019-05-17
Total Pages: 489
ISBN-13: 3030108198
DOWNLOAD EBOOKThe asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Author: Maciej Zworski
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 448
ISBN-13: 0821883208
DOWNLOAD EBOOK"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: Victor Ivrii
Publisher: Springer Nature
Published: 2019-09-11
Total Pages: 736
ISBN-13: 3030305457
DOWNLOAD EBOOKThe 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 and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.
Author: Pablo Miranda
Publisher: Springer Nature
Published: 2020-11-12
Total Pages: 272
ISBN-13: 3030555569
DOWNLOAD EBOOKThis proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.
Author: Alex Barnett
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 354
ISBN-13: 0821853198
DOWNLOAD EBOOKThis volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.
Author: Aref Jeribi
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-03-22
Total Pages: 228
ISBN-13: 3110598191
DOWNLOAD EBOOKThis proceedings volume collects select contributions presented at the International Conference in Operator Theory held at Hammamet, Tunisia, on April 30 May 3, 2018. Edited and refereed by well-known experts in the field, this wide-ranging collection of survey and research articles presents the state of the art in the field of operator theory, covering topics such as operator and spectral theory, fixed point theory, functional analysis etc.
Author: Philippe Blanchard
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 223
ISBN-13: 0817682023
DOWNLOAD EBOOKThis volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.
