howdy folks

@Skyler, hello

@heather how goes the life of our rising star

@Skyler, far from rising star, but well, thank you. How about you?

@heather idk, going from quadratic equation to eigenvalues is quite a jump

on my end im really ready to be able to spend a month on winter break, but I have one important meeting before that tomorrow

good luck in that!

(the meeting, I mean)

but yes, I am also looking forward to winter break, though it'll be a bit shorter than yours.

meanwhile I'd be really happy to see if there were some condensed matter folks on chat

Theoretical CM?

@DanielSank It's the same in the end ;P

@DanielSank eh, its not really anything too high level

at least yet

@Skyler condensed structured or unstructured matter? :D

@Sanya structured, metallic systems mainly

the easy stuff :p

@Skyler I know a bit on that

some of the questions I'm looking at are pretty easy stuff I've forgotten, others build up more since I'm doing kinetics

But mostly on spin chains at the advanced level

for example

Using dropbox on a shared limited storage system is a pain in the ass!!!

@G.Bergeron im looking at this problem where I have lamellar Cu and Au planes, infinite pattern

stacked on each other

Dropbox tries to cache my full dropbox which fills the whole disk quota...

ok

there are two intuitions for the solution I have

solution to what problem?

Either you get a simple tapering off, or there were cases where sometimes when you're dealing with material interfaces you get a a rapid depletion from the interfaces

Ill make a quick sketch

band structure?

concentrations

so those were suppose to look a tad more periodic

Ok what are looking for? (and what is c(x)?)

C(x) is concenration

and I'm trying to make C(x,t)

so time evolution basically

Where the time evolution is given by hopping terms?

When talking about condensed matter, you usually are talking about electronic band structure, you are not asking exactly the same type of questions and I want to be sure what you want...

Or is it in liquid phase?

@G.Bergeron picture alternating plates of copper and silver

Yes

macroscopic, so my actual problem Im solving is kinetics, but there were two different ways this answer can go, motivated by thermo and CMT

But then concentration of what are you talking about?

If it's the metal themselves, on a very long timescale there can be a diffusion process.

You've given me an initial condition of some system, but not clue as to what dynamics we are talking about...

@G.Bergeron say concentration of silver

yea

this is a diffusion problem

@G.Bergeron my bad, diffusion

With hard metal? Or liquid?

@G.Bergeron metal, hard

those are the two ways I could see this system diffusing

where you just gradually diffuse to a stead concentration, or you deplete rapidly at interfaces due to a high chemical potential, then eventually reach the same $t -> \infinity$ final state

Ok

The two cases would be separated by the relation between the average hopping probability in the bulk and into each other.

man my latex is rusty

Something like this, I think: If the diffusion on a timescale where the system can reach local equilibrium, then it's the first, otherwise, it's the second

@G.Bergeron whats the scale you mean when you're referring to local

like in non-equillibrium thermo you assume that you have local equillibrium?

and derive Onsager relations

To separate them, you would need to posit some kind of criteria based on how ''steep'' the free energy is due to the difference in chemical potential

@G.Bergeron can you think of the type of functional form the second type of solution could take though

for the first one I know I can construct the solution pretty easily from superpositioning solutions to the Heaviside

Your system is globally not equilibrium, so the scale would be much smaller than the scale of a significant variation in the concentration (macro variable) but much bigger than the lattice scale.

and another thing, I know that chemical potential is treated at continuous for solutions of the second form

@Skyler It's something like a shockwave solution

And you would release entropy

@Skyler Yeah first one is like the heat equation in the end

@G.Bergeron havent worked with shockwave solutions, is there a formal name I should search for?

You could derive a model by considering small cubes as equilibrium system that interacts on the boundary

@G.Bergeron technically in the t to infinity limit wouldnt both look the same

@G.Bergeron quick derpy question

I don't know much about shocks, maybe look at en.wikipedia.org/wiki/… to start

lets say I solve it in the first case

simply a diffusion problem

and I was going to solve it as a superposition of heaviside functions

what do I use for boundary conditions?

@Skyler Not necessarily... Suppose a gas is expended slowly (because of diffusion limits or a wall) then the final state is not the same as explosive decompression

Because you extracted work instead of dumping it in heat

Oh, but I guess in your case it could be the same though, as nothing is working on anything...

can I just use the BCs for a standard solution of a heaviside problem then superposition solutions

But maybe just keep that in mind. If there is something else then an adiabatic evolution, then your thermodynamic evolution cannot only be described by a potential and the path to reach a particular state is important!

@Skyler Just convolute the heat kernel with step functions

or do it by Fourier transform

@G.Bergeron basically here you get each step function sinusoid term multiplied by a exponential decay in time right

Or what you did

kind of something like that, yeah

@G.Bergeron the fourier series would probably be easier to write though

now that i think about it

easy peasy

thanks

btw, you familiar with spinodal decomposition?

may want to pick at your brain a little bit later when I go over some notes