- #1

kelly0303

- 563

- 33

Now assume I connect the trap to a resonant RLC circuit, with resonant frequency ##\omega_0##, at temperature ##T##, such that the motion of the particle is damped with a damping coefficient ##\gamma##. Now the motion can be simply described by a damped harmonic oscillator equation.

However, I am interested in how the thermal noise of the circuit comes into play. I read a bit about noise theory and there is a pretty straight forward formula for the noise spectrum as a function of the frequency. However I am interested in how does the uncertainty in the position at a given time t is affected by the noise.

Of course we can't precisely tell the position anymore, as the thermal noise is random, but I would like to assign an uncertainty to it. Basically, I have ##z(t)## from the damped harmonic oscillator formula and I would like to add to it a ##dz(t)##, which is the uncertainty for a given time and position (as a function of probably ##\gamma## and ##T##). How can I do this? Thank you!