Mathematical and Theoretical Physics Seminar

Abstract: It is a fascinating idea that the wave function in relativistic quantum physics could be a function psi(x_1,...,x_N) involving one spacetime variable x_i per particle, hence N time variables t_i = x_i^0, i = 1,2,...,N. As natural as it may sound, this concept of "multi-time wave functions" leads to a range of challenging physical and mathematical problems, such as: How can one define a consistent and interacting time evolution in the multiple time (x_i^0) variables? Which types of PDEs work for that? What is the physical meaning of |\psi|^2 at unequal times? Can one reformulate quantum field theories using multi-time wave functions?, and: Are there new possibilities for evolution equations which are specific to the multi-time formalism? This talk will provide a non-technical overview of recent progress concerning these questions.

Abstract: Our work on complex systems is analyzed by methods from nonlinear dynamics and statistical physics. We are interested in the versatile role of noise such as order-by-disorder effects and novel effects which would be absent without noise. Another fundamental role is played by frustration of interaction loops. We point out why the concept of frustration is generic and more generally applicable than in the familiar context of spin glasses. With examples from coupled oscillatory units we shall illustrate how frustrated couplings can considerably enrich the phase space and lead to similar effects as in spin glasses. We briefly discuss ongoing work on predator-prey games with a dynamic generation of multiple spatial and temporal scales and very interesting applications.