Table of Contents
Preface ix
Acknowledgments xii
Author biographies xiii
1 Introduction 1-1
1.1 Classical mechanics 1-2
1.2 Rise of quantum mechanics 1-7
1.3 Eugene Wigner 1-13
1.4 Modern devices and simulation 1-16
1.5 Our approach 1-17
References 1-18
2 Approaches to quantum transport 2-1
2.1 Modes and the Landauer formula 2-5
2.2 The scattering matrix approach 2-9
2.3 The density matrix 2-13
2.4 Green's functions 2-21
2.5 What are the relative advantages? 2-27
References 2-32
3 Wigner functions 3-1
3.1 Preliminary considerations 3-2
3.2 The equations of motion 3-5
3.3 Generalizing the Wigner function 3-8
3.4 Other phase space approaches 3-11
3.5 Wigner-Weyl transforms 3-15
3.6 The hydrodynamic equations 3-18
References 3-21
4 Effective potentials 4-1
4.1 Size of the electron 4-2
4.2 The Bohm potential 4-6
4.3 Bohm and the two-slit experiment 4-11
4.4 The Wigner potential 4-14
4.5 Feynman and effective potentials 4-17
References 4-23
5 Numerical solutions 5-1
5.1 The initial state 5-2
5.2 Numerical techniques 5-8
5.2.1 Stability and convergence 5-10
5.2.2 The boundary/contact 5-12
5.2.3 Artificial reflections 5-16
5.2.4 Spectral methods 5-17
5.3 The resonant tunneling diode: Wigner function simulations 5-21
5.4 Other devices 5-22
References 5-23
6 Particle methods 6-1
6.1 The classical Monte Carlo technique 6-2
6.1.1 The path integral 6-4
6.1.2 Free-flight generation 6-7
6.1.3 Final state after scattering 6-8
6.1.4 Time synchronization 6-10
6.1.5 Rejection techniques for nonlinear processes 6-11
6.2 Paths in quantum mechanics 6-14
6.2.1 Bohm trajectories 6-16
6.2.2 Feynman paths 6-17
6.2.3 Wigner paths 6-18
6.3 Using particles with the Wigner function 6-21
6.3.1 Weighted Monte Carlo 6-22
6.3.2 Introducing an affinity parameter 6-23
6.3.3 Signed particles 6-27
References 6-30
7 Collisions and the Wigner function 7-1
7.1 The interaction representation 7-2
7.2 The electron-phonon interaction 7-4
7.2.1 Acoustic phonons 7-4
7.2.2 Piezoelectric scattering 7-6
7.2.3 Non-polar optical and intervalley phonons 7-7
7.2.4 Polar optical phonons 7-8
7.2.5 A precautionary comment 7-9
7.3 The Wigner scattering integrals 7-9
7.4 Collisions in the Monte Carlo approach 7-11
References 7-18
8 Entanglement 8-1
8.1 An illustration of entanglement 8-3
8.2 Entanglement in harmonic oscillators 8-4
8.3 Measures of entanglement 8-10
8.4 Some illustrative examples 8-15
8.4.1 Photons 8-15
8.4.2 Condensed matter systems 8-17
References 8-20
9 Quantum chemistry 9-1
9.1 Quantum statistics 9-2
9.2 Reactions and rates 9-4
9.3 Tunneling 9-8
9.4 Spectroscopy 9-13
References 9-14
10 Signal processing 10-1
10.1 Signal propagation 10-2
10.2 Wavelets 10-6
References 10-7
11 Quantum optics 11-1
11.1 Propagation 11-2
11.2 The Jaynes-Cummings model 11-4
11.3 Squeezed states 11-8
11.4 Coherence I 11-11
11.5 Coherence II 11-14
11.6 Bell states 11-15
References 11-20
12 Quantum physics 124
12.1 The harmonic oscillator 12-2
12.1.1 The driven oscillator 12-3
12.1.2 Qubits 12-6
12.2 Quantum physics 12-7
12.2.1 Parity again 12-8
12.2.2 Quantum Hall effect 12-9
12.2.3 Qubits 12-10
12.3 Superconductivity 12-13
12.3.1 Coupling to a resonator 12-14
12.3.2 SQUIDS 12-16
12.3.3 Qubits 12-17
12.4 Plasmas 12-21
12.4.1 Kinetics 12-22
12.4.2 High-density plasmas 12-24
12.4.3 Hydrogen 12-25
12.5 Relativistic systems 12-25
12.5.1 Waves and particles 12-29
12.5.2 The strong force 12-32
12.5.3 Other forces 12-33
12.6 Quantum cascade laser 12-34
References 12-36
