Scattering of Matter Wave Solitons on Localized Potentials

Major Role of Multiscale Entropy Evolution in Complex Systems and Data Science

Complex systems are prevalent in various disciplines encompassing the natural and social sciences, such as physics, biology, economics, and sociology. Leveraging data science techniques, particularly those rooted in artificial intelligence and machine learning, offers a promising avenue for comprehending the intricacies of complex systems without necessitating detailed knowledge of underlying dynamics. In this paper, we demonstrate that multiscale entropy (MSE) is pivotal in describing the steady state of complex systems. Introducing the multiscale entropy dynamics (MED) methodology, we provide a framework for dissecting system dynamics and uncovering the driving forces behind their evolution. Our investigation reveals that the MED methodology facilitates the expression of complex system dynamics through a Generalized Nonlinear Schrödinger Equation (GNSE) that thus demonstrates its potential applicability across diverse complex systems. By elucidating the entropic underpinnings of complexity, our study paves the way for a deeper understanding of dynamic phenomena. It offers insights into the behavior of complex systems across various domains.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells

We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of controlled ejection of solitons with significantly high speeds. At the outset, we describe the scattering setup and characterize the soliton ejection in terms of the different parameters of the system. Then, we formulate a theoretical model revealing the underlying physics of soliton ejection. The model is based on energy and norm exchange between the incident soliton and a stable trapped mode corresponding to an exact solution of the governing nonlinear Schrödinger equation. Remarkably, stationary solitons can lead to high-speed soliton ejection where part of the nonlinear interaction energy transforms to translational kinetic energy of the ejected soliton. Our investigation shows that soliton ejection always occurs whenever the incident soliton norm is greater than that of the trapped mode whereas their energy is almost the same. Once the incident soliton is trapped, the excess in norm turns to an ejected soliton in addition to a small amount of radiation that share translational kinetic energy. We found that higher ejection speeds are obtained with multinode trapped modes that have higher binding energy. Simultaneous two-soliton ejection has been also induced by two solitons scattering with the potential from both of its sides. An ejection speed almost twice as that of single soliton ejection was obtained. Ejection outcome and ejection speed turn out to be sensitive to the relative phase between the two incoming solitons, which suggests a tool for soliton phase interferometry.

Critical soliton speed for quantum reflection by a reflectionless potential well

We consider the scattering of the nonlinear Schrödinger equation bright soliton by a reflectionless Pöschl-Teller potential well. We show that at the sharp transition between quantum reflection and full transmission, a single-node bound state localized at the center of the potential forms and is fully occupied. The profile and energy of the trapped mode are calculated both numerically and analytically using a variational calculation. The critical speed for quantum reflection is then determined from a delicate balance between the energy of the incident soliton and the energy of the trapped mode. We investigate the stability of the trapped mode against perturbations in its profile and position which explains the sharpness of the transition and sheds some light on the physics of quantum reflection. We show that quantum reflection by exciting the multinode trapped modes is also possible.