Quadratic Dissipative Evolution of Gaussian States with Drift

The solution of the Cauchy problem for the Gorini–Kossakowski–Sudarshan–Lindblad equation describing the irreversible quantum evolution of an $n$-particle system with a generator, which is a quadratic function in creation-annihilation operators, is reduced to the calculation of standard algebraic functions of $2n \times 2n$ matrices.