Quotes About Phase space

Superconductivity helped broaden my professional phase space. When I started my work, it was already known that magnetic fields could quench superconductivity. I found that the transition was not continuous, that superconductivity was initially enhanced in the presence of magnetic fields, then it would suddenly fall off.

In phase space the complete state of knowledge about a dynamical system at a single instant in time collapses to a point. That point is the dynamical system—at that instant. At the next instant, though, the system will have changed, ever so slightly, and so the point moves. The history of the system time can be charted by the moving point, tracing its orbit through phase space with the passage of time.

Mathematicians had to accept the fact that systems with infinitely many degrees of freedom-untrammeled nature expressing itself in a turbulent waterfall or an unpredictable brain-required a phase space of infinite dimensions. But who could handle such a thing? It was a hydra, merciless and uncontrollable, and it was Landau's image for turbulence: infinite modes, infinite degrees of freedom, infinite dimensions.