File:Position-position density matrix evolution.webm

English: This is a density matrix in position-position basis (a matrix with elements ${\displaystyle \rho _{xx'}=\langle x|\rho |x'\rangle }$) for a non-equilibrium mixed state. The system is a particle trapped in a 1D anharmonic potential well. The density matrix starts out bunched up on one side of the well, then evolves over time as the state sloshes back and forth in the potential well. This image was generated using the same computations as File:Hamiltonian flow quantum.webm, using the variable rho_x found in the source code therein.

The density matrix is complex valued and so this plot uses a hue mapping for the complex phase. Teal is positive real and red is negative real.

It contains equivalent information to the Wigner distribution evolution shown below (the two are related by the Wigner transform). While the position-position density matrix here is complex-valued and a bit confusing (it encodes position-position correlations in the wave function), the Wigner distribution is real-valued and attempts to decode the position correlations as momentum.