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Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

2009-06-05 Mathematics
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Release : 2009-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)

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Book Synopsis Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules by : AndrŽ Martinez

Download or read book Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules written by AndrŽ Martinez. This book was released on 2009-06-05. Available in PDF, EPUB and Kindle. Book excerpt: 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

2014-06-05 Mathematics
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Release : 2014-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 897/5 ( reviews)

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Book Synopsis Effective Hamiltonians for Constrained Quantum Systems by : Jakob Wachsmuth

Download or read book Effective Hamiltonians for Constrained Quantum Systems written by Jakob Wachsmuth. This book was released on 2014-06-05. Available in PDF, EPUB and Kindle. Book excerpt: 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

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 531/5 ( reviews)

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Book Synopsis Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models by : Pierre Magal

Download or read book Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models written by Pierre Magal. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-12-13 Mathematics
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Release : 2012-12-13
Genre : Mathematics
Kind : eBook
Book Rating : 660/5 ( reviews)

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Book Synopsis Microlocal Methods in Mathematical Physics and Global Analysis by : Daniel Grieser

Download or read book Microlocal Methods in Mathematical Physics and Global Analysis written by Daniel Grieser. This book was released on 2012-12-13. Available in PDF, EPUB and Kindle. Book excerpt: 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

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

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Book Synopsis Unfolding CR Singularities by : Adam Coffman

Download or read book Unfolding CR Singularities written by Adam Coffman. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 962 (first of 5 numbers)."

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