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So, we are here with the British summary of what we discussed yesterday.

First of all, today our plan is to finish a bit about a discussion of normal, unavoidable systems of interference that happen with this deviating sphere.

Then we will also discuss slightly how one can incorporate in the same formalism, very easily the effect of these collapse models that John Raybors is talking about today.

And we will focus on this coherent model, the collapse of the sphere. Very nicely put it on the same framework.

And then we will focus on the second vector, the quadratic coordinates.

And then the third one will be on saying, okay, let's now assume that we can put these particles to the ground state and then switch off the graph and start to see how coherently the center of mass extends.

And whether we can compare the mass to the positions and whether this can be used to solve the five collapse models or what are the limits and so on.

And then it's time allows, and I would like also to show you just a very recent discussion we are doing, on a particular proposal on how to do this with the limits.

Good. So the summary, we discussed the other day about this position localization type of decode. And as you remember, this was just saying that all the other terms of the density matrix

are proved to be a function of time with this function. The exponential decay is a function of time. And this was this localization, but this is the decay weight that can be written in a very general way.

It depends on two parameters, small gamma and capital H. And we gave an interpretation that small gamma was the scattering weight of particles.

And 2 times 8 was the growing wavelength of the particle that comes from the mass. As you can see, just to make a rapid connection, this is the localization scattering weight and the localization resource.

This will be perfectly the same for the CSL models, but we also have two constants. How much frequency of localization events and how much you localize.

But in our case, we show that it will also extract the scattering of normal particles in the same manner as mass of localization, both of them are molecules.

From here there was a limit, which is when the separation distance is much more than 2A, I can approximate this. And then this looks like alpha, sorry, gamma, force H squared squared.

And this we call capital lambda. And the other limit, then this limit we call the long wavelength, because the wavelength of the scatter is very long, so we do not resolve the separation in the wave function.

And the other regime makes this to be constant and it will be equal to the scattering weight.

For that limit, for the long wavelength approximation, this master equation that leads to this decodidensary can be written in that way.

Which is a master equation that also is more than you have seen many times, and it was called diffusion.

And this appears in the long wavelength approximation. Good. So then what we started to do last day was to discuss these four particular scenarios.

And we showed that actually when we derived our theory of cavity-equity with the light-pianosphere, there was a thermal field, there was a light scattering, the scattering of photons.

And the particle in this creates some kind of cavity. And this we saw that had the form of this localization parameter, this diffusion with a ray given by, sorry for the camera, but I will write the rays here.

So the localization due to a light scattering was given by the polarization square, the intensity of the field, in the case of the tweezers for instance, we use the tweezers.

And then we saw that a particular radiation that will always be there even if you don't use any laser is blackout in radiation. And in that case, for the case of blackout radiation,

in that case this was proportional to the radius to a power of 6, ht, h bar c, and the temperature is the environmental temperature to a power of line, the speed of light, and the effect and this coefficient because with the fraction index and the relevant frequency of the blackout.

And this was the idea. So in blackout radiation there is also two additional effects. So this effect is just elastic scattering of blackbody radiation photons.

But apart from elastic scattering, an object always has some temperature and if it has some temperature it means that the charges inside the object are not vibrate. And if a charge vibrates it makes water.

This I will now have to give you just a moment because this has to be done with this microscopic UV and with the

Just believe me that one can also show what is the emission rate of a particle and then this emission rate also plays a role. Because if I put a photon here and I put a mass and then I put in 4 pi, I just diffuse. That's regarding emission. And also absorption.

So as soon as the charge is fluctuated, then the polarization of the particle fluctuates and according to the fluctuation dissipation theorem, it should also dissipate and dissipate will be related to the imaginary part of the fraction index.

And this will also mean that you also absorb photons even though you do not only elastically scatter them. And these two give also every time you absorb a photon you also get a heat cut.

So all of these also plays a type of polarization type of equivalence and in that case the rate is like depending on either emission or absorption. And this goes like C to the volume.

And the emission will depend on the internal temperature and if it's a photon of the external temperature to the power of 6 and now depending on the imaginary part of the refractive index.

So the process that you just described, you emit photons and for pi you have diffusion. Is that enough to explain that you have this fluctuation dissipation theorem? You need additional process to absorb photons?

My question is that I want to answer that this diffusion is... No, it's that both processes, the process of emitting photons and absorbing photons are related to the imaginary part of the reflection index and at least comes from the equation in the equation.

Ok, I'm trying to formulate it more precisely. So when you emit photons, you get a kick and it diffuses until you get a heat cut.

I would have said that this is the fluctuation dissipation theorem by itself. Yeah, that would then apply for the center of mass. My comment was just to tell you because suddenly now I have to introduce the imaginary part of the reflection index and so far all I said was valid even if the reflection index is totally real.

So the lambda VD is the diffusion due to black body radiation hitting. Elastic scattering. Elastic scattering and the other one is emission of black body radiation. Emission and absorption.

So the difference is that one will depend on the internal temperature of the particle and the other on the external temperature.

Because it's the temperature of the incoming photons and the other is the temperature if you want to emit any photons. So if you were to try to put that term into the Hamiltonian, like for the light scatter you were able to show how that term would come from the Hamiltonian just by defining the electric field in a certain way.

How would you distinguish in a Hamiltonian between an elastic scattering case versus an absorption? So the theory is slightly different. So in that it's very important you have to do what is called a quantized electromagnetic field in the presence of the electric matter.

And then this is what is called this microscopic 3D. And then you would see this phenomenon arising from the fact that the polarization of the particle, so the response of the particle to an external field, it has a steady state response that leads to the electric constant plus some fluctuation.

And this fluctuation can come either from the cerebral fluctuations of the charges or also from the quantum fluctuations of the charge. The second leads to Casimir forces, the first one leads to the normal black body radiation.

This is a bit beyond the Hamiltonian at that world because there I was just assuming the polarization to be real.

Right. I was more asking like between the absorption versus the scattering of black body radiation because it seems like it's all black body radiation so how would you distinguish between these two?

Yeah, well, you mean physically? So what happens is the three physical processes which are different, elastic scattering of photons, emission of photons, or absorption of photons, the three of them lead to diffusion with the rate equal by this.

Can you comment quickly please about internal and external temperature? I don't know if you can give some example of that. Sure, this is crucial.

So because what we have to do with this is that we say, oh great, we don't have plenty of bosses, they are not connected to anything.

But that's a very good of course, but it also means that as soon as you put energy into the sphere, into the internal modes, it can only release this energy by black body emission and that's a very slow process compared to emission because I'm in contact with another material.