Macroscopic quantum tunneling /

Table Of Contents:
Preface viii
Acknowledgements x

Introduction 1(16)

The cat and the moon 1(3)

Leggett program 4(2)

What is meant by ``macroscopic''? 6(3)

Intuitive consideration 6(1)

S-Cattiness 7(2)

Macroscopic quantum tunneling 9(8)

Leggett program and macroscopic quantum tunneling 9(4)

Classification of macroscopic quantum tunneling: MQC and MQT 13(3)

Exercises 16(1)

Overview of macroscopic quantum tunneling 17(24)

Standard form of Hamiltonian and Schrodinger equation: dimensional analysis 17(3)

Overview of MQC 20(5)

Overview of MQT 25(5)

Formulas for ground-state energy splitting and decay rate 30(2)

Quantum decay and irreversible processes 32(2)

Euclidean action: bounce and instanton 34(7)

Exercises 38(3)

Some candidate systems for macroscopic quantum tunneling 41(54)

SQUID 41(12)

Josephson junction and equivalent circuit for SQUID 41(3)

Phase difference and magnetic flux 44(2)

Equation of motion for magnetic flux 46(1)

Naive quantum theory 47(5)

Friction coefficient 52(1)

Liquid 3He-4He mixture 53(19)

Phase separation in liquid 3He-4He mixture 53(3)

Rayleigh--Plesset model 56(2)

Naive quantum theory 58(4)

Field theory of nucleation 62(10)

Single-domain magnet 72(23)

Naive quantum theory 74(3)

Longitude basis and longitude-represented wavefunction 77(5)

Longitude representation of spin operator 82(3)

Longitude-represented Schrodinger equation and its consequences 85(3)

Symmetry and interference effect 88(3)

Exercises 91(4)

Environmental problems 95(22)

Coherence and decoherence 95(1)

General discussion of dephasing in MQC 96(6)

Dissipative environment 102(4)

Non-dissipative environment 106(4)

Quantum Zeno effect 110(7)

Exercises 114(3)

Harmonic environment 117(16)

Linearly-coupled harmonic-environment model 117(3)

Heisenberg equation of motion: part 1 120(3)

Environmental frequency distribution function 123(1)

Retarded resistance function 124(2)

Heisenberg equation of motion: part 2 126(2)

Equation of motion in the classical regime 128(5)

Exercises 131(2)

Quantum resonant oscillation in the harmonic environment 133(18)

Preliminary consideration on perturbation theory 133(5)

Perturbation theory of time evolution 138(5)

Macroscopic quantum resonant oscillation 143(4)

Estimation of quantum-resonance frequency 147(4)

Exercises 149(2)

Quantum decay in the harmonic environment 151(10)

Conjectures on decay rate 151(1)

Euclidean action functional and bounce 152(5)

Effective Euclidean action functional and a stationary point 153(1)

Effective Euclidean action functional in the harmonic-environment model 154(3)

Bounce and decay rate in a bilinear model 157(2)

Remark on decay rate at finite temperatures 159(2)

Exercises 160(1)

General versus harmonic environments 161(10)

Modified Born--Oppenheimer basis 161(3)

Modified Born--Oppenheimer representation for Hamiltonian 164(2)

Caldeira--Leggett assumption 166(5)

Exercises 170(1)

The cat in the moonlight 171(16)

Macrorealism 171(1)

Leggett--Garg inequality 172(2)

Measurable correlation functions 174(1)

Quantum-mechanical correlation function 175(2)

Thought experiment to test Leggett--Garg inequality 177(7)

Concluding remarks 184(3)

Exercises 185(2)

Appendix A. Euclidean space and Hilbert space 187(2)

Three-dimensional Euclidean space 187(1)

Hilbert space 187(2)

Appendix B. Virtual ground state of a system of a single degree of freedom and its decay 189(6)

Energy eigenfunction 189(2)

Quasi-stationary wave 191(1)

Resonance and virtual bound states 192(1)

Decay of the virtual ground state 193(2)

Appendix C. Functional derivative 195(4)

Appendix D. Miscellanea about spin 199(8)

Spin operator 199(1)

Spin-1/2 decomposition of spin S 200(1)

Spin disentanglement theorem 201(2)

Spin coherent state 203(4)
Bibliography 207(2)
Index 209