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.

Autorentext

V. M. (Nitant) Kenkre is a theoretical physicist of Indian origin (born in 1946 in Goa, then a Portuguese colony) who is a Distinguished Professor (Emeritus) of Physics at the University ofNew Mexico (UNM), USA, retired since 2016. He is known for his research primarily in three areas: coherence in the transport of quasiparticles such as excitons and electrons in molecularaggregates, interdisciplinary investigations on matters of importance to biology and ecology, for instance the spread of epidemics, and nonlinear science, particularly the discrete nonlinear Schroedinger equation in small systems. He has published a book on the first topic, Memory Functions, Projection Operators, and the Defect Technique (Springer Nature, 2021) and coauthored another on the second, Theory of the Spread of Epidemics and Movement Ecology of Animals (Cambridge University Press, 2020). The present book is on the third of thetopics mentioned. He has also coauthored a book on Exciton Dynamics in Molecular Crystals and Aggregates (Springer 1982), coedited another on Modern Challenges in Statistical Mechanics (American Institute of Physics, 2003), and published a book on his poetry entitled Tinnitus (X-libris, 2013), as well as two on philosophy: The Pragmatic Geeta and What Is Hinduism (Amazon, 2019). He has made noteworthy contributions not only to familiar research areas of physics but also to the statistical mechanics of granular materials, to the theory of microwave sintering of ceramics, and to the understanding of energy transfer in photosynthetic systems. His undergraduate studies were at the Indian Institute of Technology, Bombay (India), and his graduate work took place at the SUNY Stony Brook (USA). He was elected Fellow of the American Physical Society in 1998 and Fellow of the American Association for Advancement of Science in 2005. 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 many of whom occupy prominent leadership positions at universities worldwide and in the industry.

Inhalt

1. The Discrete Nonlinear Schrödinger Equation and the Two-State System (Dimer)2. Dimer Solutions, Mobility Reduction, and Neutron Scattering

   3. Initial Delocalization, Phase-Nonlinearity Interplay, and Fluorescence Depolarization

   4. Static Energy Mismatch in the Nonlinear Dimer: Nondegeneracy

   5. Extended Systems with Global Interactions, and Nonlinear Trapping

   6. What Polarons Owe to their Harmonic Origins

   7. Slow Relaxation: the Nonadiabatic Nonlinear Dimer

   8. Thermal Effects: Phase-Space and Langevin Formulations

   9. Microscopic Origin Issues about the DNLSE for Polarons

   10. Bose-Einstein Condensate Tunneling: the Gross-Pitaevskii Equation

   11. Miscellaneous Topics and Summary of the Book