The Ultimate Lindblad equation - American History Information Guide and Reference

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:

$\dot\rho=-{i\over\hbar}[H,\rho]-{1\over\hbar}\sum_{n,m}h_{n,m}\big(\rho L_m L_n+L_m L_n\rho-2L_n\rho L_m\Big)+\mathrm{h.c.}$

where $ρ$ 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 $γ$ is the decay rate.

Categories: Quantum mechanics | Equations

Your American History Reference Guide! - Lindblad equation

Lindblad equation

Your American History Reference Guide!
- Lindblad equation