# Definition of Ohmic bath and damping force

I have read the Wikipedia article on quantum dissipation where it is talking about the bath spectral function.

The bath spectral function provides a constraint in the choice of the coefficients $C_i$

$$J(\omega) = \frac{\pi}{2} \sum_i \frac{C_i^2}{m_i \omega_i} \delta (\omega - \omega_i)$$

The corresponding classical kind of dissipation can be shown to be Ohmic, but the definition of Ohmic is missing.

In looking for the definition of an Ohmnic bath, I only found this article:

http://www.rmki.kfki.hu/~diosi/tutorial/ohmmarkovtutor.pdf

which says

The Ohmic model applies when damping force is proportional to the instant velocity. Ohm’s Law in electricity results from such microscopic damping force on electrons moving in a potential.

Now they are defining the Ohmic model with the damping force. I have not found anything about the damping force. I do not know if that is the force that releases the heat from the system.

1. In the case of quantum dissipation, and the spectral function, what is the definition of Ohmic? What does that mean practically?

2. What do they mean by damping force?

• The definition of Ohmic is missing but looks pretty obvious if you read the next sentence. Essentially it seems it means $J(\omega) \sim \omega$. – thermomagnetic condensed boson Jul 16 '18 at 19:46