Conversation started May 11, 2017 at 10:51.
Emilio Pisanty
Emilio Pisanty
May 11, 2017 10:51
Are the group theorists around?
Wrichik Basu
Wrichik Basu
I don't need any more help. I've understood. I'll help myself as I've always done.
Kenshin
Kenshin
@ShaVuklia
@WrichikBasu iawa jokin
@ShaVuklia it is better in this case however to look at the probabilty density of survival (as opposed tod ecay)
Sha Vuklia
Sha Vuklia
lol @Wrichik that's life. we're all on our own:P
Emilio Pisanty
Emilio Pisanty
@Slereah you do groups, right?
Slereah
Slereah
>implying probabilities make sense in a non-frequentist sense
Sha Vuklia
Sha Vuklia
May 11, 2017 10:52
oh really? @Kenshin
Kenshin
Kenshin
yeah
Slereah
Slereah
Bayesians get out
Kenshin
Kenshin
if f(x) is probablity density of survival
Slereah
Slereah
@EmilioPisanty To some degree
Kenshin
Kenshin
then integral of f(x)dx is probability of survival over range of integration
then if youw ant probabilty of death/decay
it is probabilty of surving * probability of dying just after
this will hopefully make sense as you progress through the topic maybe
Sha Vuklia
Sha Vuklia
May 11, 2017 10:53
lol i'm only asking because of this mean time :P
Kenshin
Kenshin
just keep in mind, the probabilty of surviving from A to B and Bto C is the multiplicative
Emilio Pisanty
Emilio Pisanty
@Slereah I'm looking for some reference that classifies the subgroups of $U(1)\times U(1)$
Kenshin
Kenshin
but this doesn't work for dying
@ShaVuklia yeah these concepts are required to derive mean time
Emilio Pisanty
Emilio Pisanty
in principle shouldn't be too hard, right?
but it's turning out very hard to google
I'm obviously doing it wrong
Sha Vuklia
Sha Vuklia
okay but i get it @Kenshin because for dying, you first need to have lived
Kenshin
Kenshin
May 11, 2017 10:54
yea
Sha Vuklia
Sha Vuklia
so you multiply
Slereah
Slereah
Wouldn't the subgroups of $U(1) \times U(1)$ just be the product of the subgroups of $U(1)$?
Kenshin
Kenshin
like probablity of dying at time between X and dX is probabilyty of surving to X then dying between X and dX
Slereah
Slereah
I think the subgroups of $U(1)$ are mostly gonna be discrete rotations
Sha Vuklia
Sha Vuklia
yes got it
Slereah
Slereah
May 11, 2017 10:55
Although there's also the... rational rotations, I think?
And irrational rotations
Kenshin
Kenshin
coolz
Emilio Pisanty
Emilio Pisanty
@Slereah I'm mostly looking for copies of $U(1)$ which "wind" multiple times
Slereah
Slereah
Those also form subgroups
Balarka Sen
Balarka Sen
@EmilioPisanty Sure, S^1 x S^1 is as a group isomorphic to R^2/Z^2.
Take a line with rational slope on R^2, and quotient down.
Emilio Pisanty
Emilio Pisanty
@BalarkaSen so I should just google for R^2/Z^2?
Or maybe it's just subsets of the type $\{(e^{ip\theta},e^{iq\theta}):\theta\in\mathbb R\}$ for $p,q\in \mathbb N$, and no more mystery?
oh well
Balarka Sen
Balarka Sen
May 11, 2017 11:02
@EmilioPisanty Those are the closed non-discrete subgroups. You still have to take account to the discrete ones (which are all isom to Z/m x Z/n)
There are also non-closed subgroups (which are all isom to R)
user129412
user129412
I'm looking for a graduate level solid state textbook with emphasis on mesoscopic physics, topics such as nanowires for example. Anyone here particularly fond of a specific book? I've had a look at Semiconductor Nanostructures by Thomas Ihn, which is nice and rather elaborate in that a lot of topics are covered, but quite superficial. I'd look for a little more detail perhaps.
Slereah
Slereah
@BalarkaSen Is that the rotations by $\theta \in \Bbb R \setminus \Bbb Q$
Balarka Sen
Balarka Sen
@Slereah a rotation is not a subgroup... it is quotient of a line of irrational slope on R^2, yes.
It's a real line which wraps around the torus a lot. Eg in Emilio's representation, plug in $p = 1$, $q = \sqrt{2}$.
 
Conversation ended May 11, 2017 at 11:07.