Dissipation function in fluctuation dissipation theory

[Jeffrey Yang]

Hello every:

Actually, there are 2 questions.

The first one is how to understand the dissipation function used in the fluctuation dissipation theory. I notice that for a dielectric material with a complex dielectric function, this dissipation function will be the imaginary part of the dielectric function. Does this imply that we need to trace the absorption process and finally get the correct dissipation function in a thermal equilibrium situation?

The second question is, does this dielectric function used here consider the effect of environment? We know that we can modify the photonic environment and further modify the absorption and emission process. One typical example is the modification of the local density of states. Once this LDOS is modified, do we need to define an effective dissipation function here? For example, if the LDOS is enlarged for 10 times and we assume the occupation number is always the maximum, this means in equilibrium the absorption will also be enlarged for 10 times. Now, shall we consider an effective dissipation function which will be 10*Im{eps} now?

Thanks for the discussion.

 

[eljose79]

Hello there,

Thank you for your questions regarding the dissipation function used in the fluctuation dissipation theory and its consideration of the environment. I can provide some insight and clarification on these topics.

To answer your first question, the dissipation function in the fluctuation dissipation theory is used to describe the energy loss or dissipation in a system due to thermal fluctuations. In the case of a dielectric material with a complex dielectric function, the dissipation function is indeed the imaginary part of the dielectric function. This is because the imaginary part of the dielectric function represents the energy dissipation due to the absorption of photons by the material. So, in a thermal equilibrium situation, tracing the absorption process and obtaining the correct dissipation function is necessary to accurately describe the system.

Moving on to your second question, the dielectric function used in the fluctuation dissipation theory does take into account the effect of the environment. This is because the dielectric function is dependent on the material's properties as well as the surrounding environment. So, if the photonic environment is modified, the dielectric function will also change accordingly. In your example of modifying the local density of states, this would indeed result in a change in the dielectric function and in turn, the dissipation function. So, in this case, an effective dissipation function that takes into account the modified environment would need to be defined.

I hope this helps clarify your questions. If you have any further inquiries, please do not hesitate to ask. Thank you for your interest in the fluctuation dissipation theory.