The evolution of Liouville von Neumann master equations in the Pechukas–Yukawa framework

This paper presents a novel formalism for the out-of-equilibrium dynamics of the density matrix, capable of describing highly entangled many-body interactions. The evolution of quantum states is evaluated via eigenvalue dynamics of a general Hamiltonian system, perturbed by a parametrically evolving variable λ(t) that carries the time-dependence. This is achieved using the Pechukas–Yukawa mapping of the evolution of the energy levels governed by their initial conditions on a generalized Calogero–Sutherland model of a 1D classical gas. As such, quantum systems can be described exactly in their entirety from eigenvalue dynamics. Under this description, we provide an improved understanding of the relationship between nonequilibrium quantum phase transitions and decoherence, which has significant impacts on a wide range of applications.