Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules PDF Download
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Author: Andr Martinez
Publisher: American Mathematical Soc.
ISBN: 082184296X
Category : Mathematics
Languages : en
Pages : 96
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Book Description
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: Andr Martinez
Publisher: American Mathematical Soc.
ISBN: 082184296X
Category : Mathematics
Languages : en
Pages : 96
Get Book Here
Book Description
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: Jakob Wachsmuth
Publisher: American Mathematical Soc.
ISBN: 0821894897
Category : Mathematics
Languages : en
Pages : 96
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Book Description
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.
Author: Pierre Magal
Publisher: American Mathematical Soc.
ISBN: 0821846531
Category : Mathematics
Languages : en
Pages : 84
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Book Description
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.
Author: Daniel Grieser
Publisher: Springer Science & Business Media
ISBN: 3034804660
Category : Mathematics
Languages : en
Pages : 147
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Book Description
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.
Author: Adam Coffman
Publisher: American Mathematical Soc.
ISBN: 0821846574
Category : Mathematics
Languages : en
Pages : 105
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Book Description
"Volume 205, number 962 (first of 5 numbers)."
Author: Gelu Popescu
Publisher: American Mathematical Soc.
ISBN: 0821847104
Category : Mathematics
Languages : en
Pages : 137
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Book Description
"Volume 205, number 964 (third of 5 numbers)."
Author: Huaxin Lin
Publisher: American Mathematical Soc.
ISBN: 0821851942
Category : Mathematics
Languages : en
Pages : 144
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Book Description
"Volume 205, number 963 (second of 5 numbers)."
Author: Michael Thoreau Lacey
Publisher: American Mathematical Soc.
ISBN: 0821845403
Category : Mathematics
Languages : en
Pages : 87
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Book Description
"Volume 205, number 965 (fourth of 5 numbers)."
Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821847759
Category : Mathematics
Languages : en
Pages : 178
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Book Description
"Volume 205, number 966 (end of volume)."
Author: Zeng Lian
Publisher: American Mathematical Soc.
ISBN: 0821846566
Category : Mathematics
Languages : en
Pages : 119
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Book Description
The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
