Friction at zero temperature? By the fluctuation-dissipation theorem (detailed-balance for Langevin equation), $$\sigma^2 = 2 \gamma k_B T$$ where $\sigma$ is the variance of noise, $\gamma$ is a friction coefficient, $k_B$ is Boltzmann's constant, and $T$ is temperature. So in principle, one can have $\gamma\neq 0$ while $T=0$ and $\sigma=0$.
Is it indeed possible to experimentally achieve a system whose temperature and noise approach zero, but whose friction coefficient $\gamma$ does not approach zero?


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*If yes, what would be an example of such a system? What is the physical source of friction for such a system?

*If not, why not? Is there some sort of "quantum" correction to the fluctuation-dissipation theorem that rules out such zero-noise, non-zero friction systems?

 A: Mechanical friction is a perfectly fine example. The coefficient of friction between two materials does not approach zero at absolute zero.
Electrical resistance (as pointed out by Alexander) is another example. Some materials (superconductors) have zero resistance at absolute zero, but by no means all of them!
I would say that $\gamma \neq 0$ while $T=0$ and $\sigma=0$ is the "default" expectation that occurs most of the time. Things like superconductivity and superfluidity are interesting surprises that go against the normal expectation.
The physical sources of friction at absolute zero are generally the same as the physical sources of friction at other temperatures. For example, electrical resistance can come from electrons bumping into grain boundaries or impurities or defects etc. Mechanical friction comes from phonons (vibrations) that are created as the two materials rub against each other ... same as usual.
If a source of friction is temperature-dependent, it can either increase or decrease as you approach absolute zero.
A: A simple approximation of your question, from the semiclassical point of view, could be this. 
Imagine a ball running over a surface. This surface is made up of other little balls: these balls are considered little respect to the one running over them so they create a flat surface. Imagine that these little balls start to moving up an down: the surface won't be flat and we call what is experienced by the big ball in this way "friction".
So let the little balls be independent quantum harmonic oscillators. You find out that the energy of one of these is $E=h\nu (n+1/2)$. For the ground state, $T=0K$ and $n=0$ and $E=h\nu/2$. So it's not zero.
So at $T=0K$ there is still a remaining movement of the atoms of the lattice that constitute the surface and so they can cause friction in the sense said before.
A: Isn't the friction here the mechanical analogy to the resistance in a circuit? At $T=0$ the voltage noise is zero but you still have the finite property 'resistance'. 
In more general terms, the dissipation is given by the imaginary part of a generalized susceptibility $\chi$ of your physical system. So as long as your system can dissipate energy you can have non-zero friction at any temperature. 
An example is a particle in a liquid under Brownian motion (fluctuation and dissipation for Brownian motion).
A: The Langevin equation is introduced to modelize the motion of particles under the influence of a random gaussian force. If T=0, there is no motion at all and no friction γ*u !!!! 
In any case, the equation σ2=2γkBT holds for a given γ
