Abstract:
Semiclassical theory of Bloch particles has provided the basis for our understanding of crystalline metals, semiconductors and insulators. Berry curvatures deform the phase-space symplectic structure into a non-canonical form, and are accountable for a large number of thermodynamic and transport phenomena in solid state physics. In this talk, I will extend our theory into spacetime crystals, taking an atomic chain with a phonon mode as an example, and obtain a set of geodynamic equations of motion for an event wavepacket in the phase space of spacetime and their reciprocals. I will also consider the case with crystal deformation, discuss how an associated lattice connection may seamlessly combine with the Berry connection to establish a covariant semiclassical theory, with applications on the issue of flexo-electricity and magnetism, etc. My talk will end with a geodynamic formulation for a deformed spacetime crystal, and its surprising formal simplicity compares well with the elegance of particle dynamics in general relativity.