lindblad equation

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

\rho

(such as ensuring normalisation and hermiticity of

\rho

). It reads:

-{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.}

where

\rho

is the density matrix,

H

is the hamiltonian part,

L_m

are operators defined by the system to model as are the constants

h_{n,m}

. The most common Lindblad equation is that describing the damping of a quantum harmonic oscillator, it has

L_0=a

L_1=a^{\dagger}

h_{0,1}=-(\gamma/2)(\bar n+1)

h_{1,0}=-(\gamma/2)\bar n

with all others

h_{n,m}=0

. Here

\bar n

is the mean number of excitations in the reservoir damping the oscillator and

\gamma

is the decay rate.

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