The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is
among the most fundamental problems in statistical physics. Recent theoretical studies have …

This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

This is a review on theoretical and experimental studies on dielectric microcavities, which
play a significant role in fundamental and applied research. The basic concepts and theories …

From the reviews:" This book is concerned with the application of methods from dynamical
systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a …

This textbook presents a modern account of turbulence, one of the greatest challenges in
physics. The state-of-the-art is put into historical perspective five centuries after the first …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

Based on a Brown University course in applied mathematics, this rigorous and demanding
treatment focuses on specific analytical methods. It emphasizes nonlinear problems …

1.1. Introduction to conjugacy problems for diffeomorphisms. This is a survey article on the
area of global analysis defined by differentiable dynamical systems or equivalently the …