Dynamics and Statistical Mechanics of Long-Range Interacting Particles in a Parametrically Driven Periodic Potential
This event is part of the Biophysics/Condensed Matter Seminar Series.
Abstract: It is well known that some driven systems undergo transitions when the system parameter is changed adiabatically around its critical value. This transition can be due to the change in the topological structure of the phase space, called a bifurcation. Depending on the type of change in the topological structure, such transitions are well classified in the theory of bifurcations. Among the driven systems, the parametrically driven periodic potentials (PDPP) are particularly interesting due to the intimate coupling between its time and spatial components. A unique example of such a system is Kapitza's pendulum, which is a pendulum with an oscillating suspension point that can be made to stand stably in the inverted position for certain driving frequency and amplitude. In this talk, I will present our work on understanding the dynamical behavior of multiple particles interacting through the simple Coulomb repulsion in a PDPP 1D potential. It is found that the tools of statistical mechanics may be important to the study of such systems, instead of bifurcation theory, in order to understand the transitions that occur in the chaotic regime. Though the Coulomb and, similarly, the gravitational interactions of particles are prevalent in nature, these long-range interactions are not well understood from the statistical mechanics perspective because they are not extensive or additive. I will also present a simple model for understanding long-range interacting pendula, finding interesting non-equilibrium behavior of the pendula angles. Namely, that a quasistationary clustered state can exist when pendula angles are initially ordered by their index.