Interplay of Quantum Mechanics and Nonlinearity

This book presents an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE), with particular emphasis on spatially small systems that permit analytic solutions. In many quantum systems of contemporary interest, the DNLSE arises as a result of approximate descriptions despite the fundamental linearity of quantum mechanics. Such scenarios, exemplified by polaron physics and Bose-Einstein condensation, provide application areas for the theoretical tools developed in this text. The book begins with an introduction of the DNLSE illustrated with the dimer, development of fundamental analytic tools such as elliptic functions, and the resulting insights into experiment that they allow. Subsequently, the interplay of the initial quantum phase with nonlinearity is studied, leading to novel phenomena with observable implications in fields such as fluorescence depolarization of stick dimers, followed by analysis of more complex and/or larger systems. Specific examples analyzed in the book include the nondegenerate nonlinear dimer, nonlinear trapping, rotational polarons, and the nonadiabatic nonlinear dimer. Phenomena treated include strong carrier-phonon interactions and Bose-Einstein condensation. This book is aimed at researchers and advanced graduate students, with chapter summaries and problems to test the reader's understanding, along with an extensive bibliography. The book will be essential reading for researchers in condensed matter and low-temperature atomic physics, as well as any scientist who wants fascinating insights into the role of nonlinearity in quantum physics.

Presents uncommon insights into the role of nonlinearity in quantum physics Enriched with exercises to hone the reader's skills and understanding Provides powerful analytical tools and illustrates the theory with diverse applications

Autorentext
V. M. (Nitant) Kenkre is Distinguished Professor (Emeritus) of Physics at the University of New Mexico (UNM), USA, retired since 2016. His undergraduate studies were at IIT, Bombay (India) and his graduate work took place at SUNY Stony Brook (USA). He was elected Fellow of the American Physical Society in 1998, Fellow of the American Association for Advancement of Science in 2005 and has won an award from his University for his international work. He was the Director of two Centers at UNM: the Center for Advanced Studies for 4 years and then the Founding Director of the Consortium of the Americas for Interdisciplinary Science for 16 years. He was given the highest faculty research award of his University in 2004 and supervised the Ph.D. research of 25 doctoral scientists and numerous postdoctoral researchers. Through 270 published papers, his research achievements include formalistic contributions to non- equilibrium statistical mechanics, particularly quantum transport theory, observations in sensitized luminescence and exciton/electron dynamics in molecular solids, and solutions to cross-disciplinary puzzles arising in spread of epidemics, energy transfer in photosynthetic systems, statistical mechanics of granular materials, and the theory of microwave sintering of ceramics. He has interests in comparative religion, literature and visual art, and has often lectured on the first of these. His most recent coauthored book is Theory of the Spread of Epidemics and Movement Ecology of Animals (Cambridge University Press, 2020). He has also coauthored a book on exciton dynamics (Springer, 1982), coedited another on modern challenges in statistical mechanics (AIP, 2003), and published a book on his poetry entitled Tinnitus, and two on philosophy: The Pragmatic Geeta, and What is Hinduism.

Inhalt
Chapter 1. The Discrete Nonlinear Schrödinger Equation and the Two-State System (Dimer).- Chapter 2. Dimer Solutions, Mobility Reduction, and Neutron Scattering.- Chapter 3. Initial Delocalization, Phase-Nonlinearity Interplay, and Fluorescence Depolarization.- Chapter 4. What Polarons Owe to their Harmonic Origins.- Chapter 5. Static Energy Mismatch in the Nonlinear Dimer: Nondegeneracy.- Chapter 6. Extended Systems with Global Interactions, and Nonlinear Trapping.- Chapter 7. Slow Relaxation: the Nonadiabatic Nonlinear Dimer.- Chapter 8. Thermal Effects: Phase-Space and Langevin Formulations.- Chapter 9. Microscopic Origin Issues about the DNLSE for Polarons.- Chapter 10. Bose-Einstein Condensate Tunneling: the Gross-Pitaevskii Equation.- Chapter 11. Miscellaneous Topics and Summary of the Book.<p