Rizzi Real-Time Quantum Dynamics of Electron-Phonon Systems

1. Auflage 2018
ISBN: 978-3-319-96280-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 184 Seiten

Reihe: Springer Theses

This book develops a methodology for the real-time coupled quantum dynamics of electrons and phonons in nanostructures, both isolated structures and those open to an environment. It then applies this technique to both fundamental and practical problems that are relevant, in particular, to nanodevice physics, laser-matter interaction, and radiation damage in living tissue.The interaction between electrons and atomic vibrations (phonons) is an example of how a process at the heart of quantum dynamics can impact our everyday lives. This is e.g. how electrical current generates heat, making your toaster work. It is also a key process behind many crucial problems down to the atomic and molecular scale, such as the functionality of nanoscale electronic devices, the relaxation of photo-excited systems, the energetics of systems under irradiation, and thermoelectric effects. Electron-phonon interactions represent a difficult many-body problem. Fairly standard techniques are available for tackling cases in which one of the two subsystems can be treated as a steady-state bath for the other, but determining the simultaneous coupled dynamics of the two poses a real challenge. This book tackles precisely this problem.

Autoren/Hrsg.

Rizzi, Valerio

Inhaltsverzeichnis

1;Supervisors’ Foreword;7
2;Abstract;9
3;Acknowledgements;10
4;Contents;11
5;Abbreviations;14
6;1 Introduction;16
6.1;References;21
7;2 Physical Motivation;23
7.1;2.1 Radiation Damage;23
7.1.1;2.1.1 Radiation Damage in Metals;25
7.1.2;2.1.2 Radiation Damage in Biological Systems;27
7.2;2.2 Ultrashort Laser Heating of Metals;30
7.3;References;34
8;3 Simulating Electrons and Phonons: Effective Temperature Methods;37
8.1;3.1 An Effective Temperature Model for Radiation Cascades;38
8.2;3.2 The Two-Temperature Model (2TM);39
8.3;3.3 The 2TM in MD Simulations;42
8.3.1;3.3.1 Augmented MD Models, the Langevin Equation;44
8.3.2;3.3.2 Inhomogeneous Models;46
8.4;References;50
9;4 Simulating Electrons and Phonons: Atomistic Methods;52
9.1;4.1 A Simple Classical Model and the Born-Oppenheimer Approximation;53
9.2;4.2 Ehrenfest Dynamics;55
9.2.1;4.2.1 A One-Sided Electron-Atom Heat Exchange;58
9.3;4.3 Correlated Electron-Ion Dynamics (CEID);60
9.3.1;4.3.1 CEID Simulations;62
9.4;4.4 The Bonca-Trugman Method;66
9.5;References;68
10;5 The ECEID Method;70
10.1;5.1 The Model;70
10.2;5.2 An Exact Form of ?(t) and ?(t);72
10.3;5.3 The Approximations;75
10.4;5.4 ECEID's Equations of Motion;76
10.5;5.5 From Many-Electron to One-Electron Equations of Motion;78
10.6;5.6 Total Energy Conservation;79
10.7;5.7 Open Boundaries in ECEID;80
10.8;5.8 Implementing ECEID in a Computer Simulation;81
10.8.1;5.8.1 Code Breakdown;82
10.9;References;83
11;6 ECEID Validation;84
11.1;6.1 Comparison with an Exact Simulation;84
11.1.1;6.1.1 An Exact Limit on a 2-Level System with 1 Oscillator;86
11.1.2;6.1.2 Extension to a 3/Many-Level System with 2 Oscillators;88
11.2;6.2 Mimicking an Extended System and Energy Conservation;91
11.3;6.3 Validating the Open Boundaries;92
11.4;6.4 Joule Heating;93
11.4.1;6.4.1 A Microscopic Ohm's Law;96
11.4.2;6.4.2 Onsite Disorder;99
11.5;6.5 Code Performance;101
11.6;References;105
12;7 Thermalization with ECEID;106
12.1;7.1 The System;108
12.2;7.2 An Entropic Definition of Temperature;108
12.3;7.3 Comparison with Ehrenfest Dynamics;109
12.4;7.4 Results;110
12.4.1;7.4.1 Thermalization;110
12.4.2;7.4.2 Population Inversion;110
12.4.3;7.4.3 Kinetic Model;111
12.5;References;114
13;8 Inelastic Electron Injection in Water;117
13.1;8.1 Water Molecule;118
13.1.1;8.1.1 A Simple Water Model;118
13.1.2;8.1.2 Embedding Setup;120
13.1.3;8.1.3 Elastic Transmission;121
13.1.4;8.1.4 ECEID Comparison with Elastic Averages;123
13.1.5;8.1.5 The Landauer and the High Mass Limit;127
13.1.6;8.1.6 Current Assisted Phonon Heating;130
13.2;8.2 Water Chain;132
13.2.1;8.2.1 The Model;132
13.2.2;8.2.2 Simulation Details;135
13.2.3;8.2.3 Electron-Pulse Injection;136
13.2.4;8.2.4 Electron-Gun Injection;138
13.2.5;8.2.5 Eigenstate Lifetime and Band Edge Trapping;140
13.3;References;142
14;9 A New Development: ECEID xp;144
14.1;9.1 A Canonical Transformation;144
14.2;9.2 Exact Dynamics;146
14.3;9.3 The Approximations and ECEID xp;148
14.4;9.4 An Ehrenfest-Like Condition for x?(t);150
14.5;9.5 A Test Case;152
14.6;9.6 Code Performance;156
14.7;9.7 Final Remarks;156
14.8;References;158
15;10 Conclusions and Perspectives;159
15.1;References;162
16;A Electronic Operators in ECEID: From Many-Body to Single Body;163
17;A.1 Tracing Over the Electrons;163
18;A.2 Tracing the ECEID Many-Body EOM;164
19;Appendix B Open Boundaries in ECEID;167
20;B.1 General Formalism;167
21;B.2 Elastic Transmission;169
22;B.3 Including the OB in ECEID;170
23;B.4 Imposing a Constant Bias in the Leads;171
24;B.5 Other Injection Setups;173
25;Appendix C An Alternative Water Chain;174
26;C.1 Simulation Details;174
27;C.2 Electron-Pulse Injection;177
28;C.3 Electron-Gun Injection;179
29;C.4 Eigenstate Lifetime and Bandedge Trapping;179
30;Appendix D Beyond the Double (De)excitation Approximation;182
30.1;References;184