Nonlinear differential dynamics of Gaussian States
Julio A. López-Saldívar, Margarita Aleksandrovna Man'ko, Vladimir I. Man’ko · AIP conference proceedings · 2021
The dynamics of Gaussian states for systems with Hamiltonians, quadratic in the position and momentum operators, gives rise to the definition of a system of nonlinear coupled differential equations for the density matrix parameters of the system states. In this work, we show that, using the Gaussian-state covariance-matrix evolution, it is possible to solve the system of these nonlinear equations. Some examples of applications of the method developed are given for one- and two-dimensional quadratic-system Gaussian states. It is noted that this formalism can also be used to find new constants of motion related to the covariance matrices of quadratic systems.