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Author : Mouez Dimassi,Johannes Sjöstrand
Publisher : Unknown
Page : 241 pages
File Size : 48,6 Mb
Release : 2014-05-14
Category : SCIENCE
ISBN : 1107362792
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author : Mouez Dimassi,J. Sjostrand
Publisher : Cambridge University Press
Page : 243 pages
File Size : 54,5 Mb
Release : 1999-09-16
Category : Mathematics
ISBN : 9780521665445
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author : Johannes Sjöstrand
Publisher : Springer
Page : 496 pages
File Size : 40,5 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9783030108199
The 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.
Page : 448 pages
File Size : 50,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821883204
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author : Pablo Miranda,Nicolas Popoff,Georgi Raikov
Publisher : Springer Nature
Page : 272 pages
File Size : 44,9 Mb
Release : 2020-11-12
Category : Mathematics
ISBN : 9783030555566
This 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.
Page : 354 pages
File Size : 48,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853191
This 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
Page : 228 pages
File Size : 50,8 Mb
Release : 2021-03-22
Category : Mathematics
ISBN : 9783110598193
This 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,Gianfausto Dell'Antonio
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9780817682026
This 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.
Author : Victor Ivrii
Publisher : Springer Nature
Page : 889 pages
File Size : 42,7 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305574
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 general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.
Author : Oleg N. Kirillov,Dmitry E. Pelinovsky
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 49,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781118577547
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics, and dissipation-induced instabilities are treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches. Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory. Contents 1. Surprising Instabilities of Simple Elastic Structures, Davide Bigoni, Diego Misseroni, Giovanni Noselli and Daniele Zaccaria. 2. WKB Solutions Near an Unstable Equilibrium and Applications, Jean-François Bony, Setsuro Fujiié, Thierry Ramond and Maher Zerzeri, partially supported by French ANR project NOSEVOL. 3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems, Richard Cushman, Johnathan Robbins and Dimitrii Sadovskii. 4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities, Olivier Doaré. 5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field, Sergey Yu. Dobrokhotov and Anatoly Yu. Anikin. 6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials, Nir Dror and Boris A. Malomed. 7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation, Yasuhide Fukumoto, Makoto Hirota and Youichi Mie. 8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance, Igor Hoveijn and Oleg N. Kirillov. 9. Index Theorems for Polynomial Pencils, Richard Kollár and Radomír Bosák. 10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches, Paolo Luzzatto-Fegiz and Charles H.K. Williamson. 11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows, Sherwin A. Maslowe. 12. Continuum Hamiltonian Hopf Bifurcation I, Philip J. Morrison and George I. Hagstrom. 13. Continuum Hamiltonian Hopf Bifurcation II, George I. Hagstrom and Philip J. Morrison. 14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model, Philip J. Morrison, Emanuele Tassi and Cesare Tronci. 15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators, Francis Nier. 16. Stability Optimization for Polynomials and Matrices, Michael L. Overton. 17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations, Dmitry E. Pelinovsky. 18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden Instabilities, Zensho Yoshida and Philip J. Morrison. About the Authors Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor for the journal Frontiers in Mathematical Physics. Dmitry E. Pelinovsky has been Professor at McMaster University in Canada since 2000. His research profile includes work with nonlinear partial differential equations, discrete dynamical systems, spectral theory, integrable systems, and numerical analysis. He served as the guest editor of the special issue of the journals Chaos in 2005 and Applicable Analysis in 2010. He is an Associate Editor of the journal Communications in Nonlinear Science and Numerical Simulations. This book is devoted to the problems of spectral analysis, stability and bifurcations arising from the nonlinear partial differential equations of modern physics. Leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics present state-of-the-art approaches to a wide spectrum of new challenging stability problems. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics and dissipation-induced instabilities will be treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches. All chapters contain mechanical and physical examples and combine both tutorial and advanced sections, making them attractive both to experts in the field and non-specialists interested in knowing more about modern methods and trends in stability theory.
Author : André Bach
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 47,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475744958
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Author : Bernard Helffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 55,8 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9781107032309
Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.
Author : Andr Martinez,Vania Sordoni
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 44,9 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821842966
The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.
Author : Bernhard Kramer
Publisher : Springer
Page : 644 pages
File Size : 40,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540449461
The 2001 Spring Meeting of the 65th Deutsche Physikalische Gesellschaft was held together with the 65. Physikertagung, in Hamburg, during the pe riod March 26 30 2001. With more than 3500 conference attendees, a record has again been achieved after several years of stabilisation in participation. This proves the continuing and now even increasing, attraction of solid state physics, especially for young colleagues who often discuss for the first time their scientific results in public at this meeting. More than 2600 scientific pa pers were presented orally, as well as posters, among them about 120 invited lectures from Germany and from abroad. This Volume 41 of "Advances in Solid State Physics" contains the written versions of half of the latter. We nevertheless hope that the book truly reflects the current state of the field. Amazingly enough, the majority of the papers as well as the discussions at the meeting, concentrated on the nanostructured solid state. This re flects the currently extremely intensive quest for developing the electronic and magnetic device generations of the future, which stimulates science be sides the challenge of the unknown as has always been the case since the very beginning of Solid State Physics about 100 years ago.
Author : Erik P. van den Ban,Johan A.C. Kolk
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 42,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817682446
Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields. Written in his honor, the invited and refereed articles in this volume contain important new results as well as surveys in some of these areas, clearly demonstrating the impact of Duistermaat's research and, in addition, exhibiting interrelationships among many of the topics.