Phase Space Crystals
Lingzhen Guo
Abstract
This book aims to develop a general framework of condensed matter theory in phase space, instead of configuration space, of a dynamical system. Different from Euclidean real space, phase space is embedded with symplectic geometry in classical mechanics or noncommutative geometry in quantum mechanics. Arbitrary lattice Hamiltonians and crystalline many-body states in phase space can be created with the Floquet approach. The book covers topics ranging from dynamical systems, Floquet theory, topological physics to quantum many-body physics and time crystals. The book fills in the blanks in the study of dynamical systems by considering many-body physics in the phase space. Key features • First book on phase space crystals • Covers both the basics and up-to-date research of condensed matter in dynamical systems • Contains systematic and comprehensive content for beginners • Relevant to multiple physics communities including quantum physics and nonlinear science.