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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.
Table of Contents
1 Introduction
2 Dynamical Systems
3 Phase Space Lattices
4 Many-body Physics in Phase Space
5 Phase Space Crystal Vibrations
6 Time Crystals
A Phase Space Lattices
B Phase Space Interactions
C Phase Space Crystal Vibrations