Dynamical Emergence of Complex Structures in Field Theories

Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the interactions that respect those symmetries. Formally one can then quantize the system to find the masses of the fundamental excitations, but this procedure generally destroys much information about solutions of the field equations with large non-perturbative amplitudes. To get information about the properties of the solutions to these field theories without perturbative approximations we use real time lattice simulations where complex spatiotemporal structures emerge dynamically from excess free energy and a thermal background. We present results in 2 and 3 dimensions of new interacting quasi-particle formations from a quench. These objects show an emergent level of complexity which we attempt to categorize and define in a manner that should be useful to many different applications.