Recent content by Frank Castle

Thanks for the reference. So do particle velocities become correlated due to a common collisional history? And by correlated it is meant that their velocity components become related as a result of the collision between them. Is this right?

But what is intuitively meant by their velocities being correlated? Is what I wrote in post #23 a correct intuitive understanding?

Thanks for the clarification. When it is said that particle velocities become correlated during a collision is it meant that the velocities become related in such a way that, if one reverses their subsequent trajectories (i.e. flips the sign of their velocities), they will both return to the...

My understanding is that the velocities of two particles that participate in a binary collision become correlated during the collision in the sense that if one reverses the time evolution (i.e. flip the signs of their velocities), then the two particles will return to the collision point.

How is this the case though? How can they become correlated during the collision but not afterwards? Is some amount of coarse graining assumed, such that the timescale over which the correlation is lost is much smaller than the timescale over which the system evolves? Edit: Having read about...

Ok, thank you. I’ll take a look.

Right, good point. They become correlated during the collision and remain so afterwards until they collide with another particle. As far as I understand, the molecular chaos assumption is that the momenta of two particles that mutually interact are uncorrelated before they interact (i.e. any...

Sorry, I think my title was a bit misleading. I'm trying to understand this in the context of constructing Boltzmann transport equations and the molecular chaos assumption. This being said, is what I written about why the momenta of the particles become correlated after a collision correct at all?

Right. But the momenta of the two particles after the collision are correlated in the general sense, in that their momenta have become related by the collision - if I reverse the trajectories (i.e. I flip the signs of both of their momenta) of the two particles they will meet back at the...

This confuses me, as I’ve been reading these http://www.damtp.cam.ac.uk/user/tong/kintheory/kt.pdf, in particular, at the bottom of page 22 and start of page 23 the author discusses correlations between the moments of two particles that have collided. Surely the momenta of individual pairs of...

See for example http://www.damtp.cam.ac.uk/user/tong/kintheory/kt.pdf at the bottom of page 22 and start ion page 23.

So in general, is it their momenta that become correlated? Is what I wrote for why they become correlated correct at all?

Reading about molecular chaos, it is always mentioned that particle velocities become correlated after colliding.

I have been reading up on the kinetic theory of gases, and I'm unsure whether I have correctly understood why particle velocities become correlated after colliding. Is it because during the collision they exchange momentum and thus their velocities (and hence trajectories) are altered in a...

Ok, thanks for the info. So is the following a correct derivation of the Lie derivative of the volume form? $$\mathcal{L}_{X}\left(\sqrt{-g}d^{4}x\right)=\mathcal{L}_{X}\left(\sqrt{-g}\right)d^{4}x+\sqrt{-g}\mathcal{L}_{X}\left(d^{4}x\right)\\...