Interplay of Quantum Mechanics and Nonlinearity: Understanding Small-System Dynamics of the Discrete Nonlinear Schroedinger Equation

This book provides an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE) with an emphasis on spatially small systems that permit analytic solutions. It discusses the interplay of the initial quantum phase with nonlinearity, leading to novel phenomena with observable implications in fields such as fluorescence depolarization of stick dimers, rotational polarons, and Bose-Einstein condensation. It is aimed at researchers and advanced graduate students and includes chapter summaries, problems, and an extensive bibliography.

Format: Paperback / softback
Length: 310 pages
Publication date: 29 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the intricate realm of the discrete nonlinear Schrödinger equation (DNLSE), focusing on spatially small systems that enable analytic solutions. Despite the fundamental linearity of quantum mechanics, the DNLSE emerges as an approximation in numerous quantum systems of contemporary interest. Examples include polaron physics and Bose-Einstein condensation, where theoretical tools developed in this text find practical applications.

The book begins with an introduction to the DNLSE, using the dimer as an illustrative example. It then develops fundamental analytic tools such as elliptic functions, providing insights into experimental observations. The interplay between the initial quantum phase and nonlinearity is explored, leading to novel phenomena with observable consequences in fields like fluorescence depolarization of stick dimers.

Subsequent chapters analyze more complex and/or larger systems, including the nondegenerate nonlinear dimer, nonlinear trapping, rotational polarons, and the nonadiabatic nonlinear dimer. The book addresses phenomena such as strong carrier-phonon interactions and Bose-Einstein condensation.

Designed for researchers and advanced graduate students, this book includes chapter summaries, problems for testing comprehension, and an extensive bibliography. It serves as a vital resource for condensed matter and low-temperature atomic physics researchers, as well as anyone interested in gaining fascinating insights into the role of nonlinearity in quantum physics.

Weight: 516g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030948108
Edition number: 1st ed. 2022