@TobiasFünke miao miao hath a signed copy~

oops, it wasnt 3 authors

does anyone know where a precise discussion of polarization of electromagnetic waves can be found?

I am looking in Zangwill and the discussion seems prohibitively specialized.

What isn't precise in the standard treatment?

Zangwill specializes to real unit vectors to describe polariation

but that is also the standard treatment elsewhere... maybe not as explicitly so, but the usual $\varepsilon^i$ nonsense is about unit vectors.

the circular polarization basis is complex, though

so immediately the presentation is contradictory.

i ended up working out the polarization business myself though. i think im satisfied with what i ended with

That is because it is necessary

Of course, if you want to totally avoid complex numbers, you can, but it will be tremendously ugly and tedious

do note that even though the linear polarisation is clearly easier to present to students with everything real valued, circular polarisation is the one that is a lot less likely to make conceptual mistakes, easier to work simple problems out.

if i use circular polariation basis vectors $\frac{1}{\sqrt{2}} (\hat{e}_1 \pm i\hat{e}_2)$, then do i need to convert back into the $\hat{e}_i$ basis to actually compute the field, though? (In particular to take the real part)

Well, if you had used the convenience of complex basis vectors, then, yes, your scheme would be tainted by complex numbers and it will take some finessing to re-establish real-valued-ness. I don't think you can just take the real part, though that will at least be some answer.

@naturallyInconsistent yeah, I remember ;)

and I did not mean Pines and Nozières but another one, oops. anyway, does not matter ^^

lol

actually they do it wrongly, too, I think. Interesting.

do what wrongly?

grading all these labs about harmonic oscillators really hertz

...I must be really drained if I'm finding that funny

@SirCumference it is ok, it is actually funny, just that it is inappropriate for us to be enjoying your suffering

lol

@naturallyInconsistent my comment concerned the use of the Kramers-Kronig relations for the dielectric function (say, of a homogeneous system) $\epsilon(q,\omega)$

we yesterday had the discussion about why the dielectric function is a complex quantity

@TobiasFünke miao miao knows, miao miao read the chat logs. Miao miao wanted to say something, but work had been busy

:d I see

@TobiasFünke Since I told you yesterday, I created the room but it's lenghty

Although I don't know how to invite people

Okay, I'll have a look. Can you tell me the name of the room?

@TobiasFünke "Discussion about RPA"

@TobiasFünke what is the title of this book?

@SillyGoose Vignale's book is the Quantum Theory of the Electron Liquid

@SillyGoose yes (attention, the Pines and Nozieres reference was wrong). So stick to Vignale; or check the paper I've mentioned some comments before, or "The dielectric function of the homogeneous electron gas" by Gorobchenko et al. (there should be a suitable preview on Google Books) section 2.1

God i hate when category paper just put Schreiber's big book in the bibliography

It's a thousand pages, can I get a page number maybe

Oh okay thank you both

why do we ignore the $\partial_t \vec{D}$ term in the boundary condition for $\vec{H}$?

@SillyGoose literally explained in the screenshot...

sneeepppuuu

i mean that is not an explanation

can you explain how that is an explanation? it is just words saying that the term vanishes. i don't see how it is generically true that $\partial_t \vec{D}$ has the decay behavior that is required for the "explanation" to be an explanation.

@SillyGoose $$\exists M\in\mathbb R^+\quad|\vec D|<M\qquad\implies\qquad\exists B\in\mathbb R^+\quad|\partial_t\vec D|<B$$ $$\implies\left|\int_S\mathrm da\ \hat{\vec n}\cdot\frac1c\partial_t\vec D\right|<wB/c\to0$$ as $w\to0$

I have some confusion regarding this plot. first, i only see how the second plot shows something typical of resonance, namely that there is a sharp peak at some $\omega$ value, but this is all that sticks out to me. is there smth im missing for why the top part shows typical resonance behavior as well? second, the second plot (which is in line with my expectation) [...]

[...] is associated with the imaginary component. i am wondering if there's a particular reason for this? naively, id expect a priori for the real part to be the one that is in line with this expectation

@Relativisticcucumber sorry, can you rephrase your question again a bit? I don't understand

the real and imaginary parts of the dielectric constant are related by Kramers-Kronig relation (I cannot help but again to point out that this actually is not true in general, see my comments above)

@TobiasFünke well the first q is how does the top graph show behavior typical of resonances as the first line of the photo says

yes. see Kramers-Kronig relations (e.g. Wikipedia)

ok i will check. brb

the point is that the real and imaginary parts are not independent, and so this is indeed a typical situation for a resonance

ok i think i have made some progress but then one q remains which is why is the peak behavior associated with the imaginary part? presumably they could be switched, or no?

separately, this relation is quite interesting. i never knew the real and complex parts of a function are not truly independent

@Relativisticcucumber this does not hold for every function, of course

@Relativisticcucumber mathematically I guess the answer is yes. Physically no. The peak in the imaginary part is physical. you consider the Drude/Lorentz oscillator model?

@TobiasFünke erm sorry can you expand on this a bit? i have seen the drude model

what physical model do you consider/show in the plot you've attached?

the peak, roughly, means that the greatest absorption appears at/near the resonance frequency...I guess this is quite physical, no?

you have to consider what the real and imaginary parts of $\epsilon$ mean...and from that, try to interpret the plot (e.g. where is the peak? what does a peak mean?)

(barring in mind the model you consider...of course for real materials or so, it does not look so nice and might look quite different)

@TobiasFünke oh oh wait can i say that the imaginary component is physically responsible for the attenuation of the wave i.e. describes how the material sucks the energy out of the wave, and then this happens at a particular frequency bc, similar to what nI said before & silly goose, certain frequencies support transitions so "on resonance" frequencies facilitate transitions in the material and as a result take the energy. [...]

[...] then we can justify the graph of the real part by the KK relations that you mentioned?

this seems reasonable. i hope ive finally got it

wouldn't a general relativistic mollusk be more appropriate?

@think_meaning_buildß i do love dumbo octopi

:D

wait that was a jab right? @think_meaning_buildß

nah

then what is the logic for why relativistic mollusk would be more appropriate

i thought u were calling me stupid lol

oh i thought u were saying i was snail brain

bc nI said this info like 2 days ago

lmfao

yeah i was lurkin' when he said it >8(

xD

i love all animals

but i also love vegetables

my other aliases have been harmonicpickle and glassnoodle

good lawd, the amount of woo around quantum topics online makes it practically inpenetrable to those of us without a proper quantum background.

maybe i should be grateful it's not my field or i think i'd have spasms everytime i open a browser