Dynamics of the Density Cube

Density cube theory extends the canonical quantum density matrix $\rho_{ij}$ with the addition of an extra index to $\rho_{ijk}$. The elements of the density cube with two different indices, $\rho_{iij}$ and $\rho_{ijj}$, correspond to the real and imaginary parts of the off-diagonal element $\rho_{ij}$ of the density matrix and describe double-path interference, while those with three different indices describe non-canonical triple-path interference. In this letter, we propose an equation of motion for the density cube, obtained from the quantization of ternary Nambu dynamics, and find that pairs of triple-path interferences oscillate into each other.