Every physicist has a pretty clear idea of how to define equilibrium phases of matter (e.g. using free energy considerations), whether disordered or ordered (and if ordered, a variety of situations can be encountered). By contrast, dynamics-wise, no generic and clear-cut definition a dynamical phase (disordered, intermittent, uniform, ergodicity-breaking, pattern-forming, etc) can be found. Instead, one works on a system-to-system basis.
I will illustrate, on the simple example of a classical system of mutually excluding particles diffusing on a line, how a robust definition of what a dynamical phase is can be achieved. As I will go along, we will see that there may even exist transitions between dynamical phases. On a formal level, these dynamical transitions have everything in common with the quantum phase transitions that appear in hard-condensed matter.
I will show that, in turn, approaching quantum problems with a classical eye, can, even with the simple example I'll discuss, lead to unexpected progress on the quantum side.
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