This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of...

This book highlights a comprehensive and self-contained account of the physics of Rydberg atoms and their integration within the broader framework of cavity quantum electrodynamics (QED) and hybrid quantum systems. Rydberg atoms in cavities constitute a uniquely powerful and versatile platform for exploring strongly interacting quantum systems, where the combination of exaggerated atomic properties and engineered light matter coupling enables access to physical regimes that are otherwise unattainable. With their exceptionally large electric dipole moments, long radiative lifetimes, and...