ATOMIC THEORIES

By N. RAMAK

SECTION I INTRODUCTION TO QUANTUM ELECTRODYNAMICS Chapter 1 Boson Model of Quantized EM-Field and Nature of Photons3 Abstract3 Introduction 4 Results And Discussion 6 Conclusions 13 References15 SECTION II SCATTERING PROCESSES Chapter 2 On a Theory of Light Scattering From a Bose-Einstein Condensate19 Abstract19 Introduction 20 Scattering Problem in Conditions of Quantum Degeneracy 20 Polariton Propagator 23 Conclusion 26 Acknowledgements 26 References 27 Chapter 3 Analytical Property of Scattering Matrix: Spectroscopy Phenomena and Sharp Overlapping Autoionization Resonances29 Abstract30 Introduction30 Results and Discussions32 TABLE OF CONTENTS Conclusion45 Contributions48 References 49 Chapter 4 Deep Inelastic Scattering On Ultracold Gases53 Abstract53 Popular Summary54 Introduction55 High-Momentum Behavior of The Dynamic Structure Factor63 Sum Rules At Large Momentum Transfer73 Line Shift77 Dynamic Structure Factor of Bose Gases Beyond Bogoliubov82 Y Scaling of The Nondegenerate Bose Gas89 Application To Fermi Gases91 Summary And Conclusions93 Acknowledgments94 Appendices95 References102 SECTION III FERMION AND BOSON PROPAGATORS Chapter 5 Short-Time Quantum Propagator And Bohmian Trajectories111 Abstract111 Introduction112 Bohmian Trajectories113 The Short-Time Propagator114 Short-Time Bohmian Trajectories117 Conclusion119 Acknowledgements120 References 121 Chapter 6 Investigation of Free Particle Propagator With Generalized Uncertainty Problem123 Abstract123 Introduction124 Gup-Corrected Hamiltonian124 Perspicuous Form of Propagator125 Conclusion128 References130 Chapter 7 A Cosmological Bound on e+ e– Mass Difference133 Abstract133 Acknowledgements139 References 140 SECTION IV QED PROCESSES Chapter 8 Cooperative Quantum Electrodynamical Processes In An Ellipsoidal Cavity143 Abstract143 Introduction 144 Quantum Electrodynamical Model 146 Mode Functions of the Cavity and Their Semiclassical Approximation 147 Photon Path Representation154 Results 158 Conclusion 160 Acknowledgments 161 References 162 Chapter 9 Electron Paramagnetic Resonance of Single Magnetic Moment on a Surface163 Abstract163 Introduction164 Results165 Discussion170 Conclusions175 Acknowledgements 175 Author Contributions 175 References 176 Chapter 10 Exact Critical Exponents For The Antiferromagnetic Quantum Critical Metal In Two Dimensions181 Abstract181 Popular Summary182 Introduction183 Low-Energy Theory and Interaction-Driven Scaling184 Self-Consistent Solution187 Physical Observables192 Summary And Discussion196 Acknowledgments197 Appendices197 References222 SECTION V FEYNMAN DIAGRAMS AND HIGHER-ORDER INTERACTIONS IN QED OF STRONG FIELDS Chapter 11 Completeness And Orthonormality Of The Volkov States and the Volkov Propagator In Configuration Space229 Abstract229 Introduction230 The Green’s Function of the Dirac Equation in a Plane Wave232 The Green’s Function of The Dirac Equation In a Plane Wave and The Volkov Propagator243 A Proof of The Completeness And of The Orthonormality of The Volkov States246 References251 Chapter 12 Higher-Order Interactions In Quantum Optomechanics: Analytical Solution of Nonlinearity257 Abstract257 Introduction258 Theory260 Examples264 Further Considerations271 Anharmonic Oscillator275 Conclusions279 Supplementary Materials280 Acknowledgments282 References284 Chapter 13 High Precision Hyperfine Measurements In Bismuth Challenge Bound-State Strong-Field QED295 Abstract296 Introduction296 Results299 Discussion304 Methods305 Acknowledgements309 Contributions310 References 311