The Lindblad equation or master equation in the Lindblad form is the most general type of master equation allowed by Quantum mechanics to describe non-unitary (dissipative) evolution of the density matrix ρ (such as ensuring normalisation and hermiticity of ρ). It reads:
![\dot\rho=-{i\over\hbar}[H,\rho]-{1\over\hbar}\sum_{n,m}h_{n,m}\big(\rho L_m L_n+L_m L_n\rho-2L_n\rho L_m\Big)+\mathrm{h.c.}](a/../upload/math/1fe55a337dda82db3b57e7b4c904e60b.png)
where ρ is the density matrix, H is the hamiltonian part, Lm are operators defined by the system to model as are the constants hn,m.
The most common Lindblad equation is that describing the damping of a quantum harmonic oscillator, it has L0 = a, 
, 
, 
with all others hn,m = 0. Here 
is the mean number of excitations in the reservoir damping the oscillator and γ is the decay rate.