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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.
Dr Lingzhen Guo is a postdoctoral fellow at the Max Planck Institute for the Science of Light. Guo previously led a research group at the Institute of Theoretical Solid State Physics (TFP), Karlsruhe Institute of Technology (KIT). Guo carried out his Bachelor, Master and PhD studies at the Beijing Normal University, China. During the PhD project, Guo spent two years doing joint research at the Karlsruhe Institute of Technology (KIT), Germany. His research fields cover quantum optics, statistical physics and quantum many-body physics. Amongst his successful publication history, Dr Guo has authored several definitive theoretical articles on Phase Space Crystals in Physical Review Letters, Physical Review A and New Journal of Physics etc. He is known to be the world leading expert on Phase Space Crystals and has been invited to give talks on the topic at many international conferences. Dr Guo recently took a professor position at the Nanjing University of Science and Technology (NJUST), China.
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