The master equation of the damped harmonic oscillator is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

\frac{d}{dt}\rho_S(t)

=

-i\omega_0

[a^\dagger a,\rho_S(t)]

+

\gamma_0(\bar n+1)

\{

a\rho_S(t) a^\dagger

-\frac{1}{2}

a^\dagger a \rho_S(t)

-\frac{1}{2}

\rho_S(t) a^\dagger a

\}

+

\gamma_0\bar n

\{

a^\dagger

\rho_S(t)

a

-\frac{1}{2}

a a^\dagger \rho_S(t)

-\frac{1}{2}

\rho_S(t)

a

a^\dagger

\}

\equiv

\mathcal{L}\rho_S(t).

[/itex]

Is there any method to analytically find out some eigenvalues, like the smallest three eigenvalues, of the liouvillian?

I am an engineering graduate, but now a rookie in physics.

Thanks for any advices.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find the eigenvalues of Liouvillian

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**