Speaker
Description
For almost a century, the general solution for the Schrödinger equation was assumed to be generated by a time-ordered exponential known as the Dyson series. We discuss under which conditions the unitarity of this solution is broken, and additional discrete dynamics emerges. Then, we provide an alternative construction that is manifestly unitary, regardless of the Hamiltonian and the setup. The new construction involves an additional Hermitian operator with a singular time dependency and evolves in a non-gradual way. Its dynamics exhibit the behavior of a collective object governed by Liouville's equation, performing transitions at a measure $0$ set of times. Our considerations show that Schrödinger's and Liouville's equations are, in fact, two sides of the same coin, and together they become the unified description of quantum systems in the fractalic regime.
