Analytical solution of the time evolution of an entangled electron spin pair in a double quantum dot nanostructure

Using master equations we present an analytical solution of the time evolution of an entangled electron spin pair which can occupy 36 different quantum states in a double quantum dot nanostructure. This solution is exact given a few realistic assumptions and takes into account relaxation and decoherence rates of the electron spins as phenomenological parameters. Our systematic method of solving a large set of coupled differential equations is straightforward and can be used to obtain analytical predictions of the quantum evolution of a large class of complex quantum systems, for which until now commonly numerical solutions have been sought.