Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules write by Andr Martinez. This book was released on 2009-06-05. Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules available in PDF, EPUB and Kindle. 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.
Effective Hamiltonians for Constrained Quantum Systems
Effective Hamiltonians for Constrained Quantum Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Effective Hamiltonians for Constrained Quantum Systems write by Jakob Wachsmuth. This book was released on 2014-06-05. Effective Hamiltonians for Constrained Quantum Systems available in PDF, EPUB and Kindle. The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.
Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models
Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models write by Pierre Magal. This book was released on 2009. Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models available in PDF, EPUB and Kindle. Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.
Microlocal Methods in Mathematical Physics and Global Analysis
Microlocal Methods in Mathematical Physics and Global Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Methods in Mathematical Physics and Global Analysis write by Daniel Grieser. This book was released on 2012-12-13. Microlocal Methods in Mathematical Physics and Global Analysis available in PDF, EPUB and Kindle. Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.
Unfolding CR Singularities
Unfolding CR Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Unfolding CR Singularities write by Adam Coffman. This book was released on 2010. Unfolding CR Singularities available in PDF, EPUB and Kindle. "Volume 205, number 962 (first of 5 numbers)."
