From quantum to classical molecular dynamics : reduced models and numerical analysis / Christian Lubich.

Format:

Book

Author/Creator:

Lubich, Christian, 1959-

Contributor:

Rosengarten Family Fund.

Series:

Zurich lectures in advanced mathematics

Language:

English

Subjects (All):

Molecular dynamics--Mathematical models.

Molecular dynamics.

Quantum theory--Mathematics.

Quantum theory.

Numerical analysis.

Schrödinger equation.

Physical Description:

ix, 144 pages : illustrations ; 24 cm.

Place of Publication:

Zürich, Switzerland : European Mathematical Society, ©2008.

Summary:

"This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrodinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized."--Jacket.

Contents:

I. Quantum vs. Classical Dynamics

I.1. First Look

I.2. Free Schrodinger Equation

I.3. Schrodinger Equation with a Potential

I.4. Averages, Commutators, Uncertainty

I.5. Many-Body Systems

II. Reduced Models via Variational Approximation

II.1. Dirac-Frenkel Time-Dependent Variational Principle

II.2. Adiabatic / Born-Oppenheimer Approximation

II.3. Separating the Particles: Self-Consistent Field Methods

II.4. Parametrized Wave Functions: Gaussian Wave Packets

II.5. Mixed Models, Quantum-Classical Models

II.6. Quasi-Optimality of Variational Approximations

III. Numerical Methods for the Time-Dependent Schrodinger Equation

III.1. Space Discretization by Spectral Methods

III.2. Polynomial Approximations to the Matrix Exponential

III.3. Splitting and Composition Methods

III.4. Integrators for Time-Dependent Hamiltonians

IV. Numerical Methods for Non-Linear Reduced Models

IV.1. Variational Space Discretization

IV.2. Variational Splitting: Abstract Formulation

IV.3. Variational Splitting for MCTDH

IV.4. Variational Splitting for Gaussian Wave Packets

V. Semi-Classical Dynamics Using Hagedorn Wave Packets

V.1. Hagedorn's Parametrization of Gaussian Wave Packets

V.2. Hagedorn's Semi-Classical Wave Packets

V.3. Numerical Integrator for Hagedorn Wave Packets.

Notes:

Includes bibliographical references (pages 137-141) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9783037190678

3037190671

OCLC:

297500112

Publisher Number:

9783037190678