Computational Strong-Field Quantum Dynamics: Intense Light-Matter Interactions

• Publisher: De Gruyter
• Year: 2017
• Tongue: English
• Leaves: 290
• Category: Library

✦ Synopsis

This graduate textbook introduces the com-putational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time dependent Schrödinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach.

Contents

How to propagate a wavefunction?

Calculation of typical strong-field observables

Time-dependent relativistic wave equations: Numerics of the Dirac and the

Klein-Gordon equation

Time-dependent density functional theory

The multiconfiguration time-dependent Hartree-Fock method

Time-dependent configuration interaction singles

Strong-field approximation and quantum orbits

Microscopic particle-in-cell approach

• Suitable for graduate students starting a MSc or PhD in the field of strong-field quantum dynamics.
• Includes detailed explanations of the widely used numerical wavefunction propagators.
• Contains many examples.

✦ Table of Contents

Contents
Preface
List of abbreviations
I How to propagate a wavefunction?
1 Time-dependent Schrödinger equation
1.1 Time propagation and stability
1.2 Spatial discretization
1.3 Imaginary-time propagation
1.4 More dimensions: Operator splitting
1.5 Expansion in spherical harmonics
2 Scaled cylindrical coordinates
3 Employing second-quantization notion
3.1 Grid hopping
4 Summary
II Calculation of typical strong-field observables
1 Ionization rates
2 Photoelectron spectra
2.1 Energy window operator method
2.2 Spectral method
2.3 Time-dependent surface flux method
2.4 Pros and cons of the various methods for photoelectron spectra
3 Emitted radiation and high-harmonics spectra
III Time-dependent relativistic wave equations: Numerics of the Dirac and the Klein–Gordon equation
1 From nonrelativistic to relativistic quantum mechanics
1.1 Relativistic quantum mechanical equations of motion—a naive attempt
1.2 The Klein–Gordon equation
1.3 The Dirac equation
2 Free particles and wave packets
2.1 Free-particle solution of the Klein–Gordon equation
2.2 Free-particle solution of the Dirac equation
3 Numerical solution of the Dirac equation
3.1 General methods for time-dependent quantum mechanics
3.2 The split operator method
3.3 The Fourier split operator method for the Schrödinger equation
3.4 The Fourier split operator method for the Dirac equation
4 Numerical examples
IV Time-dependent density functional theory
1 A few general remarks on time-dependent many-particle methods
2 DFT for effective single-electron potentials
2.1 KS spin-DFT
2.2 Actual implementation
3 Time-dependent calculations
3.1 Time-dependent KS solver with spherical harmonics and multipole expansion
3.2 Low-dimensional benchmark studies
3.3 Where TDDFT fails in practice
V The multiconfiguration time-dependent Hartree–Fock method
1 Multiconfiguration time-dependent Hartree–Fock
2 Implementing the MCTDHF method
2.1 Uniform grids
2.2 Computation of the mean-field operator
2.3 Restricted vs unrestricted
2.4 Time integration
2.5 Computing the ground state
3 Applications of MCTDHF
3.1 Calculation of highly correlated ground states
3.2 Nonsequential double ionization
3.3 High-harmonic generation
4 Extending MCTDHF to nonuniform grids
4.1 Differentiation on a nonuniform grid
4.2 Integration on nonuniform grids
4.3 Treatment of the two-body terms
4.4 Ground state of small sodium clusters
5 Conclusion
VI Time–dependent configuration interaction singles
1 Introduction
2 Basics of TDCIS
2.1 TDCIS wavefunction
2.2 The N-body Hamiltonian
2.3 Equations of motion
2.4 Limitations
3 Implementation of TDCIS
3.1 Symmetries and orbital representations
3.2 Evaluating matrix elements
3.3 Spin-orbit interaction
3.4 Grid representation
3.5 Hartree–Fock
3.6 Complex absorbing potential
3.7 Expectation values
3.8 Ion density matrix
4 Strong-field applications of TDCIS
4.1 Subcycle ionization dynamics and coherent hole motion
4.2 Multiorbital and collective excitations in HHG
VII Strong-field approximation and quantum orbits
1 S-matrix elements
2 Strong-field approximation
3 Harmonic generation rate and ionization rate
4 Ground-state wavefunctions, rescattering potential, and multielectron effects
5 Numerical examples for harmonic and electron spectra
6 Saddle-point method
7 Classification of the saddle-point solutions
8 Numerical results for HATI spectra obtained using the SPM and uniform approximation
9 Quantum orbits
10 Summary
VIII Microscopic particle-in-cell approach
1 Basic concept
1.1 Physical problem
1.2 Particle representation
1.3 PIC approximation
1.4 MicPIC force decomposition
1.5 The MicPIC approximation
2 Numerical aspects of MicPIC
2.1 Electromagnetic field propagation with the FDTD method
2.2 Particle representation on the PIC level
2.3 Local correction
2.4 Particle propagation
2.5 Implementation of ionization
2.6 MicPIC parameters and scaling
2.7 MicPIC system energy calculation
3 Applications
3.1 Laser excitation of a solid-density foil: A simple MicPIC example
3.2 Time-resolved x-ray imaging
4 Summary
Index