Guo L. Phase Space Crystals. Condensed Matter in Dynamical Systems 2021

Textbook in PDF format

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.
Dynamical systems
Phase space lattices
Many-body physics in phase space
Phase space crystal vibrations
Time crystals
Appendix A. Phase space lattices
Appendix B. Phase space interactions
Appendix C. Phase space crystal vibrations