Matter waves inside periodic potentials are well known from solid-state physics, where
electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates …

We consider several effects of the matter wave dynamics which can be observed in Bose–
Einstein condensates embedded into optical lattices. For low-density condensates, we …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

In this work, we discuss the resonance states of a quantum particle in a periodic potential
plus a static force. Originally, this problem was formulated for a crystal electron subject to a …

Abstract The superfluidity of Bose-Einstein condensates (BECs) in optical lattices is
investigated. Apart from the usual Landau instability, which occurs when a BEC flows faster …

Abstract Superflow of a Bose–Einstein condensate in an optical lattice is represented by a
Bloch wave, a plane wave with periodic modulation of the amplitude. We review the …

We present a comprehensive analysis of the nonlinear Landau-Zener tunneling. We find
characteristic scaling or power laws for the critical behavior that occurs as the nonlinear …

A review of the structure and some properties of condensed phases of water is given. Since
the discovery of the polymorphism of crystalline ice (beginning of the twentieth century), 15 …

We investigate adiabatic evolution of quantum states as governed by the nonlinear
Schrödinger equation and provide examples of applications with a nonlinear tunneling …

We present state-of-the-art first-principles calculations of the electronic and optical
properties of silicon allotropes with interesting characteristics for applications in thin-film …