Quantum Tunneling in Complex Systems (eBook)

Preface 7
Contents 9
1 Introduction 12
1.1 Theoretical Concepts 12
1.2 Physical Systems 14
1.3 Structure of the Book 15
References 16
2 Semiclassical Approximation 17
2.1 At the Very Beginning: The WKB Approach 17
2.2 Real-time Propagator 21
2.3 Energy-dependent Propagator 25
2.4 Equilibrium Statistical Operator 26
References 28
3 Tunneling in the Energy Domain 31
3.1 Quantum Decay Rate out of a Metastable Well 33
3.2 Tunnel Splittings in Bistable Potentials 52
3.3 Tunneling in Higher-dimensional Systems 60
References 67
4 Wave-packet Tunneling in Real-time 71
4.1 Tunneling with Real Classical Trajectories? 72
4.2 Semiclassics in Complex Phase Space 74
4.3 Systematic Expansion of the HK Propagator 92
4.4 Alternative Approaches 97
References 100
5 Tunneling in Open Systems: Thermodynamical Approaches 103
5.1 Classical Kramers’ Rate Theory: A Brief Survey 104
5.2 ImF for Open Systems 108
5.3 Decay of the Zero Voltage State in Josephson Junctions 117
5.4 Tunneling of Magnetization 120
5.5 MQT in Presence of Non-Gaussian Noise 125
5.6 Dissipative Tunneling in Bistable Potentials 130
5.7 Centroid Theory 135
References 138
6 Tunneling in Open Systems: Dynamics 141
6.1 Real-time Dynamics of Quantum Dissipative Systems 142
6.2 Quantum Kramers Theory 144
6.3 Nuclear Fission 157
6.4 Alternative Dynamical Theories 161
6.5 Quantum Smoluchowski Limit 166
6.6 Applications 173
References 178
7 Unified Dynamical Theory – From Thermal Activation to Coherent and Incoherent Tunneling 181
7.1 Preliminaries 182
7.2 Parabolic Barrier 186
7.3 Double Well Potential 188
7.4 Eckart Barrier 201
References 211
8 Final Remarks and Outlook 212
References 214
Index 215