Hamiltonian , Eulerian, Tree.
So this is a Hamiltonian cycle portrait of Hamilton, and you saw these in animated form as the talk started, before the talk started.
This is a Hamiltonian cycle that looks like the letter H.
But the Hamiltonian can be reduced, if I choose a basis, to a matrix.
And so exponentiating the Hamiltonian and moving things is matrix multiplication.
So these TSP tours are Hamiltonian cycles on a complete graph.
So we've got H for Hamiltonian , E for Eulerian, T for tree.
Every one of these is a Hamiltonian cycle just with edges from that King Knight chessboard graph.
So those are the puns for the Hamiltonian cycle.
And then I build a Hamiltonian .
And if I decompose my Hamiltonian in the way that's standard for some of these systems, then essentially by linearity, I get
But the problem is if you don't talk the Hamiltonian thing, then there's not learning between organizations.
e to the minus i times a timestep times the Hamiltonian .
And the output of this is this problem Hamiltonian that you get here.
And this, that's another Hamiltonian cycle portrait of a Hamilton.
So again, I've got to start with those same Hamiltonian cycles.
This equation here, H, which is called the Hamiltonian is really the equation of everything.
And the right side tells you that this change depends on H, what is known as the Hamiltonian .
And interestingly, Europe, I think, which talks more of a Hamiltonian talk actually does more of a Jeffersonian walk.
This forms the likeness of William Rowan Hamilton, Irish mathematician, for whom the term Hamiltonian cycle is named.
Ehrenfest's Theorem says, if I have a Gaussian sitting in a potential and I evolve it using the Hamiltonian -- solve the Schrodinger equation for the motion of that
And he's doing things like taking that Hamiltonian complicated somewhat complicated equation and