The h Bar

ACuriousMind

12:00 AM

I was just about to say that you seem to be essentially asking about the Zassenhaus formula.

Mew

cool

alright so finally

I've often heared that the commutation relation completely defines the group. IS this because of that formula?

ACuriousMind

1. That's not completely true. 2. No, that's nothing to do with that.

The "commutation relations" we usually talk about are not between group elements, but between elements of the Lie algebra.

Mew

oh cos if u know the commutation relation of the group, you can derive the multiplication of any two group elements using that expansion tho

oh

take the relation [x,p] = ih

I've often herad that any representation that satisifies that relation can be used as an equivalent rep

ACuriousMind

By Lie's theorems, there is an (almost) equivalence between Lie groups and Lie algebras - all Lie groups with the same algebra have rather simple relations between them and there is a unique simply-connected group associated to each algebra.

@Mew That's another completely unrelated statement called the Stone-von Neumann theorem.

DanielSank

@EmilioPisanty cool. I'd have to review thermodynamics to understand it in details.

Mew

12:03 AM

oh, so it's specific to that relationship

so if I have another commutation relation [A,B] = something,

another gorup with the same commutation relation can't necessarily be used as a rep

unless that something = ih?

ACuriousMind

Uhhh

I'm afraid that you are using terminology far too loosely for me to be able to read that as a well-defined question.

(i.e. I have no idea what you're trying to ask)

Mew

ok, let's go back to rotations say

Now there are commutation relations that appear in the group of 3D rotations

i forget what they are hang on

ACuriousMind

Yes, $[L_i,L_j] = \mathrm{i}\epsilon_{ijk} L_k$.

Mew

yep

what is Li?

ACuriousMind

The algebra has three basis vectors, which we call $L_1,L_2,L_3$.

Mew

12:09 AM

ok

now if I find a group who's lie algebra also satisfies the above commutation relation

can I be confident that that group is equivalent to the rotation group?

ACuriousMind

@Mew No, unless you have a strange notion of equivalence.

The standard example which is relevant in quantum physics is that $\mathrm{SU}(2)$ has the same Lie algebra but is a double cover of $\mathrm{SO}(3)$, and not isomorphic to the rotation group itself.

Qmechanic

@NaveenBalaji : You should change your password. (Maybe somebody else already suggested this; I didn't read the full transcript.)

Mew

@ACuriousMind so then the rotation commutation relations don't define the rotation group?

@ACuriousMind what defines the rotation group?

in 3d

ACuriousMind

@Mew It's the group of all orthogonal 3 by 3 matrices with determinant 1.

Mew

ok

and @ACuriousMind am I right that any group with a lie algebra satisifying [x,p] = ih is equivalent?

this ithe stone-von neuman rule right?

ACuriousMind

12:16 AM

@Mew No

Mew

ok what is the stone von neumann rule?

ACuriousMind

Stone-von Neumann states that the Heisenberg group (which is the simply-connected group belonging to $[x,p]=\mathrm{i}$) has only one infinite-dimenisonal unitary representation up to isomorphism.

There may well be groups that have the same Lie algebra (quotients of the Heisenberg group by discrete subgroups, I don't know off the top of my head which ones it has) and hence also only one unitary representation, this has nothing to do with the claim.

Mew

So suppose I have a group where the lie algegbra satisfies [x,p] = i

how can i check whether it is equivallent to the Heisenberg group?

ACuriousMind

You check whether it is connected and simply-connected. If it is, it is isomorphic to the Heisenberg group, if not, it is not.

Mew

and suppose I have a group where the lie algebra satisfies [Li,Lj] = ieLk

how can I check if it is equivalent to 3d rotation?

ACuriousMind

12:23 AM

Same answer, except that it shouldn't be simply-connected but have fundamental group $\mathbb{Z}/2\mathbb{Z}$.

Do you have some actual purpose for this in mind? One is rarely given such groups with only information about their algebra but not enough information to decide whether they are the same as groups you already know

Mew

I just read in a text that stated something like, "we can see this is a representation of rotations as we can show it satisfies the commutation relations ...."

and this statement has always baffled me

ACuriousMind

And, in quantum mechanics, it doesn't matter anyway because the representations we use are projective representations which are, for most Lie groups, equivalent to linear unitary representation of their algebra.

Mew

I just found this: ocw.usu.edu/physics/classical-mechanics/pdf_lectures/21.pdf

it says:

"These are the commutation relations of infintisemal rotations. They give a complete account of the way in which successive rotations combine to give a net rotation. In essence the generators and their commutation relations define the group of rotations"

ACuriousMind

As I said, the relations between groups with the same algebra are very simple (they are all quotients of the same simply-connected group), so almost all information about a group is indeed in the algebra/commutation relations, but not all.

Mew

ah k

ACuriousMind

12:30 AM

You will often find physicists not being as precise as I am being with that statement, as you evidently already did.

Mew

i see

ty for ur hepl

DanielSank

Hi, everybody.

ACuriousMind

Hi, somebody

DanielSank

:|

@ACuriousMind give me an interesting problem, or tell me something cool.

I command you.

Mew

@ACuriousMind what does the symbol ^ mean in group theory?

ACuriousMind

12:44 AM

@DanielSank The volume of a high-dimensional ball is almost entirely concentrated near its surface, that is, the ratio of the volume of an arbitrarily thin shell (of fixed thickness) to the volume of the full ball approaches 1 as the dimension approaches infinity. I think it's cool because it shows how useless our geometric intuition is in higher dimensions.

@Mew More context, please.

DanielSank

@ACuriousMind I've heard of stuff like this before...

What is the volume of an $x$-dimensional ball of unit radius?

(let x be any real number, and use whatever analytic continuation makes sense)

ACuriousMind

@DanielSank Ah, now that might qualify as an "interesting" problem. The "nice" way is to first figure out the surface area and then integrate that from 0 to 1 to get the volume.

DanielSank

@ACuriousMind Perhaps.

I figured you'd just know the answer...

ACuriousMind

Well, I do, it's $\pi^{x/2} / \Gamma(x/2 + 1)$.

But I think the formula itself is rather boring :P

And, by the way, the exact functional form is irrelevant to see the initial fact I stated, all you need for that is that the volume of a ball goes as $\propto R^x$ with the radius.

DanielSank

1:04 AM

@ACuriousMind I will attempt to plot that formula...

It peaks near five.

How bizarre!

heather

hello everyone

DanielSank

1:21 AM

@heather hello!

heather

@DanielSank, I'm getting some good recommendations for how to fix my 2-qubit code over on the python chat =D

and I'm using git to make a branch so I don't break everything if my edits go awry (and there's a high likelihood of that happening)

I <3 github

and linux

and git

DanielSank

\(^.^)/

@heather, at some point you'll likely want to move to either a functional or object oriented code pattern.

I eagerly await to see how you develop your simulator.

Btw, warning: adding decoherence requires you to learn some new principles.

There are two ways to model decoherence and both are a bit different from what you're doing now.

It's a fascinating topic.

heather

ooh, that sounds awesome!!

DanielSank

The thing is, you can't model decoherence as a unitary operator the way you can model normal quantum dynamics.

You have to either:

1) Use a density matrix, or
2) *Average* the quantum state over many unitary evolutions where each one has random "noise" operators thrown in to model the decoherence.

Item #1 can be done with the so-called "master equation" and item #2 is called "quantum trajectories".

...or maybe "quantum jumps".

I forget exactly.

Bernard Meurer

The lyrics for my favourite song right now is just "You walk on the subway it moves around"

DanielSank

1:32 AM

They both work, but the master equation only really works for specific kinds of decoherence.

heather

@DanielSank okay, so I have two main questions here. 1. It sounds like it would be best to do the 2nd type of decoherence modeling (though it sounds a bit more difficult) - is that a correct assessment? 2. what do you mean by "function or object oriented code pattern"?

DanielSank

@heather Let's worry about modelling decoherence after you get your code working :)

As for the object oriented and/or functional approaches to programming, I think the best way to explain it is for me to make a pull request on your repo and just show how to "clean up" some of the stuff you've already done.

heather

@DanielSank, oh, by the way, you might be interested in looking at my progress on the DictFunc branch - some of the code looks a whole lot neater thanks to a suggestion in the python chatroom

DanielSank

@heather ok

user228700

1:49 AM

Hi, everyone :-)

heather

@Kaumudi, hello =)

user228700

I've a quick homework-tsy question.

user228700

I've been given that a factory produces a radioactive substance A, at a constant rate of R. A then decays into stable B, and the decay constant of this nuclear reaction is $\lambda$.

DanielSank

Hilarious finding:

The German Wikipedia page on "Quantum Computer" mistakenly calls John Martinis the founder of DWave and says he promised a universal quantum computer by 2018.

This is so wrong on so many levels.

user228700

I've found that the number of nuclei of N left undecayed is given by the function $R/\lambda (1 - e^{-\lambda t}$

user228700

1:54 AM

I've been asked to find the maximum number of nuclei A at any given point.

heather

@DanielSank, oops =P

user228700

Other than maximizing the function using calculus, what can I do to find this value? At what time will the number of nuclei be maximum? (A starts decaying as soon as it is formed)

DanielSank

@Kaumudi Calculus sound like the ticket.

That function looks wrong though.

user228700

Really? ::Checking::

user228700

:-| I did it again (the first attempt was far too messy to check for mistakes) and got the same thing, look:

user228700

2:02 AM

user228700

(Again, those are $\lamda$ s :-P)

DanielSank

@Kaumudi Check the limits.

For t=0, you get N=0.

Sounds wrong to me.

:)

user228700

Sheesh :-|

Skyler

@DanielSank its so many layers of wrong you almost have to wonder if they are somewhere wrong about being wrong on something and actually have something right in there

and why are you reading the German wikipedia page on Qunautm computers anyways?

heather

@DanielSank, the work in that branch is almost finished, just fixing a mistake and it should be ready to combine with the master branch

user228700

2:09 AM

$N = [R(1- e^{-\lambda t}) + \lambda N_{\circ} e^{-\lambda t})/ \lambda$

user228700

Phew.

Skyler

@heather what are you working on?

(late to the party)

DanielSank

@Skyler A friend read it and told me.

@heather cool

Skyler

@DanielSank that was the most likely explanation i concocted after typing that

btw Daniel, any advice for electrostatics reviewing

heather

@Skyler, I'm trying to create a simulator of a quantum computer in python 3, in a nutshell. My current problem is getting 2 qubit circuits to work properly.

I honestly didn't think you could even USE emoji in variable names. Or that there were so many different crying ones.

also, I'm trying to avoid this^

=P

Skyler

2:14 AM

@heather I still worry about this whenever I try to program anything

Physics Meta

0

Q: Downvoting a comment

Would it not be practical to also have the ability to down vote a comment as well? A bad comment can hurt the up vote of a question and is not fare that it only goes one way.

feature-request

heather

@DanielSank, I need numpy to run the program - should I just download numpy, or should I set up a whole virtualenv environment?

Skyler

my votes with just picking up SciPy since I'm pretty sure it's just a full Python environment with numpy and loads of other useful libraries added

heather

SciPy? I've never heard of that...

Skyler

scipy.org/install.html

DanielSank

2:21 AM

@Skyler eh?

@heather Are you working in a virtualenv?

@Skyler Yeah, scipy is nice.

user228700

I've one more very quick question. Am I allowed to do this:

heather

@DanielSank, currently no

Skyler

@DanielSank doing EM finally, but honestly its weird, reviewing the principles seems easy but then you start a problem and your like well I think I know nothing

heather

I think I'll just download numpy

user228700

Nvm. That's spectacularly not OK.

Skyler

2:24 AM

@Kaumudi heh

user228700

:-P

user228700

So how do I solve $e^{-\lambda t} = 0$ ? :-| I'm supposed to plug this value of $t$ into my function. However, since all my $t$ values are stuck in $e^{-\lambda t}$ form, I don't need to solve for $t$, but still...

DanielSank

@heather I definitely advocate for using virtualenv.

It's the difference between happiness and sadness.

Bernard Meurer

Yeah use virtualenv for the love of god

heather

okay, sorry! =P

Bernard Meurer

2:38 AM

You'll get some spectacular issues if you don't

heather

how do I create a virtualenv envelope (is that what you call it?)

Bernard Meurer

And unless you're me you won't enjoy fixing them

Mew

yo

@Kaumudi cool movie huh

user228700

What. A. Movie.

Mew

what's ur favourite beast

user228700

2:49 AM

I'm just going to say it: I thought it was better than all of the other HP movies.

Mew

wow

user228700

@Mew The demiguise <3

Mew

oh yeah that one's cool

user228700

You notice how it clings to Jacob? 'Cause Newt and him are friends, u see.

Mew

i like this one ^

user228700

2:50 AM

Yeah, everybody likes 'em Nifflers :-D

Mew

do u think the dude got his memory back

did u know there'a s theory that Newt = hagrid

cos they were both kicked out of hogwarts

user228700

Sorta. I mean, Newt does say that the venom only erases bad memories.

DanielSank

@heather I can help!

Mew

oh

DanielSank

One sec...

user228700

2:52 AM

And while everything that happened was a terrible memory for everybody else in the city, it was amazing for Jacob, so...

Mew

so true

user228700

@Mew Ik, Ik!

Mew

i missed that bit but makes snsese

DanielSank

@heather the road to happiness

user228700

@Mew I loved Credence <3

Mew

2:52 AM

but he was a baddie

user228700

No, he wasn't!

DanielSank

@heather read the instructions once first, then ask questions, then follow them.

user228700

I mean, he was tortured.

DanielSank

I love virtualenv, and you will too.

Mew

didn't he kill the upcoming president

user228700

2:53 AM

He did but who cares? That guy was a moron :-P

Mew

lol

he reminded me of trump tho

user228700

For anybody who doesn't want to be spoiled, please look away now.

Mew

jks

spoiler alert: Credence died

user228700

@Mew: Did u see that Credence didn't actually die?

Mew

wat?

he did die

user228700

2:54 AM

He didn't!!

Mew

he turned into feathers

how come?

user228700

There was a piece of said "feathers" that seemed to be moving of its own accord.

Mew

wow

user228700

Newt stares after it as it wisps away, at the end.

Mew

u're really observant

user228700

2:55 AM

I came home and checked and YAAAS, he didn't die!

Mew

oh that's scary

:p

user228700

They deleted a scene in which they show him boarding the same boat as Newt at the end. They said they didn't want to make it that obvious that he didn't die.

Mew

I think credence is voldamort

user228700

Nah.

user228700

Voldermort was born many many years later.

Mew

2:57 AM

do you thnk Newt is hagrid?

user228700

Although there is a rumor that baby voldermort might be in the upcoming sequels.

Mew

aww how cutre

user228700

@Mew No, but there is a theory that those two met and that it was Newt who gave Hagrid Aragog.

user228700

(Remember Aragog? It's the same spider that got Hagrid expelled and the one that has a thousand babies in the forbidden forest)

Mew

yeah I'm glad that wasn't in the movie

user228700

2:59 AM

And doood. Remember Ariana dumbledore?

Mew

nope

y?

user228700

No?

user228700

This:

user228700

Harry Potter Theory: Ariana Dumbledore Was An Obscurial

►

user228700

God, SuperCarlinBrothers are so good at HP theories.

user228700

3:01 AM

She was Dumbledore's sister, remember?

user228700

So many unanswered questions. I cannot contain my excitement for the sequels.

Mew

yeah I can't wait for the sequal too

user228700

It's gon' be goooood! :-D

Mew

is Ariana important/

user228700

Yes. VERY VERY much.

Mew

3:03 AM

why what did she do?

user228700

In the final duel b/w Grindelwald and Dumbledore (in which Dumbledore wins the elder wand, BTW), one of them casts a killing curse that kills her.

DanielSank

@heather how's it going?

user228700

That duel happened in 1945.

user228700

And the last movie of this series is set in 1945 :-D

user228700

Plus, there is heavy speculation that she herself was an Obscurial.

user228700

3:06 AM

I figured out the spoiler spoiler spoiler even before the very end. It was obvious when Mr. Graves started saying things like "Imagine what we could do together" to Credence :-P

user228700

Dood. I cannot even. So good. Especially if u understand everything.

user228700

I had to go to a bathroom stall to freak the crap out because of excitement after the movie got over (I went alone, remember? :-P)

user228700

(I haven't even discussed it properly with any of my friends yet :-( )

user228700

That's why the excitement now @Mew :-P

Mew

yeah

I don't remember the harry potter films enuf to piece together everythin

@Kaumudi if ghosts exist in harry potter, why does voldamort need horcrux?

user228700

3:10 AM

I've read the books and watched the films about 1.8 million times now :-P

Mew

oh i've never read the books

user228700

@Mew I should know this.

user228700

Something about how ghosts become ghosts in the first place.

Skyler

@DanielSank haha

this is why I just went with Anaconda

and scipy built in

user228700

@Mew: Dyou want me to completely blow ur mind?

Skyler

3:12 AM

dont even need to think about virtualenv atm

Mew

@Kaumudi yes pls

user228700

There's a theory that Fawkes, the phoenix is Dumbledore's horcrux.

user228700

ALL THE FACTS fit in perfectly.

Mew

wtf

user228700

Here:

Mew

3:13 AM

dumbedore doesn't use dark masgic tho

user228700

Harry Potter Theory: Dumbledore's Horcrux

►

Skyler

@Mew happycrux?

user228700

JKR dismissed this theory, but it's so good!

user228700

I was jumping up and down after the video :-P

user228700

@Mew Yes, but remember that duel?

Mew

3:15 AM

no soz

user228700

11 mins ago, by Kaumudi

In the final duel b/w Grindelwald and Dumbledore (in which Dumbledore wins the elder wand, BTW), one of them casts a killing curse that kills her.

Skyler

@Mew angsty teen age magister phase maybe?

user228700

Nobody knows whose wand cast that curse. It might have been dumbledore who killed his own sister. That's pretty dark.

user228700

@Skyler Lol :-P

Mew

wow

dumbledoor's bad

user228700

3:17 AM

JKR dismissed this theory, BTW.

user228700

But it could've been. I wish it were true. I mean, the facts all align so effing perfectly.

user228700

@Mew Dumbledore is so complicated.

user228700

Did u know he was gay? Had a major crush on Grindelwald. Those two were friends.

Mew

no i didn't read that bit

wow

he was friends with that dood?

user228700

Yeah.

Mew

3:19 AM

he must have a thing for bad boys

user228700

LOL, so true :-D

user228700

God, JKR is so good.

Mew

is there going to be a fantastic beasts book?

user228700

Yes yes yes!!! :-D

user228700

Going to pre-order it and everything. Cannot wait.

user228700

3:20 AM

I loved the concept of an obscurial.

Mew

yea

user228700

And most likely Ariana was one.

Mew

I liked all the cool creatures

user228700

:-D I loved the acting, zomg.

user228700

Ezra Miller <3 (Credence)

Mew

3:21 AM

what did you like about that guy?

user228700

I was able to empathize with him very deeply. He was never accepted for who he was and he trusted Grindelwald to be his friend.

user228700

He was tortured by that woman and still, for most of his life, he managed to contain his obscuria within him.

user228700

He's extremely powerful to have contained it within him.

Mew

true

user228700

I was rooting for him. I almost cried when they attacked him but I am so glad that he lives.

Mew

3:25 AM

my favourite was queenie

user228700

Yeah, Queenie was such a darling :-D

Mew

niffler

and the yoyo dragon

user228700

The yoyo dragon?! O.o The hell is that?

Mew

user228700

ROFL.

user228700

3:27 AM

You mean swooping evil xD

Mew

yeah that lol

it's cool ay

user228700

Yeah, it's very cool. Which reminds me. How amazing was that big pensieve in the death chamber or whatever?

user228700

You see all ur memories before dying :'-) So good.

Mew

yea

i thought they were just going to zap her head

user228700

I thought Avada Kedavra :-|

Mew

3:30 AM

lol yea

user228700

That bowtruckle was so cute! <3

user228700

(The little green plant he keeps in his pocket :-D)

Mew

yeah, poor guy was given away though

user228700

Yeah.

user228700

But he retrieved him!

user228700

3:32 AM

And he (the plant) was so pissed/sad xD

user228700

Newt was like "Now now, we've talked about sulking before" xD

user228700

It was actually kinda scary at times, no?

Mew

scary?

user228700

Yeah.

user228700

I mean, the scene where Shaw is killed? That was s'thing else. The marks on his face and everything. Brrr.

Mew

3:34 AM

here is why voldamort isn't a goast:

"The thing you have to remember is, for a person to become a Ghost, that person has to leave an imprint of his soul behind and choose to NOT move onto Afterlife.

But Voldemort didnt have enough of a soul to remain back. His soul was so broken, his seven other parts destroyed so fully that he only has 1/8th of a soul in Afterlife. So he can't come back as a Ghost."

user228700

Ah, I see. Thanks!

user228700

Did u expect Graves to be u know who? (Not the original u know who! :-P)

Mew

oh

lol

no i didn't

I didn't know who grendelwaard even was

user228700

I got a hint...

user228700

He gave Credence that locket. Deathly hallows.

Mew

3:36 AM

but the 7th movie was on tv after i watched FBAWTFT and I saw it mentioned him i think

is Credence mentioned in any of the harry potter books?

user228700

Deathly Hallows pt. 1? Yeah.

user228700

@Mew Nope.

user228700

Although, it's been like 5 years since I read all the books. Don't remember everything, but no, definitely no Credence.

user228700

I sorta figured when he started saying things like "Imagine what we could do together" to Credence.

user228700

Also? There's a theory that Credence is descendant from Salazar Slytherin.

Mew

3:39 AM

yeah he seems like slytherin to me

user228700

Yeah. Very much so :-P

Skyler

@Kaumudi dahells credence

user228700

Remember Luna Lovegood?

Skyler

@Kaumudi I member

user228700

@Skyler xD It's the name of a boy.

user228700

3:40 AM

Newt's grandson marries her! :-D

Mew

credence is snape's dad

user228700

And on the Marauder's map, when Harry sees Peter Pettigrew? It says "Newt Scamander" on the right, meaning he was visiting that night.

user228700

@Mew What? NO. How?!

Mew

just is

user228700

—.— Nope.

user228700

3:41 AM

No way.

Mew

lol

user228700

OK, this was awesome @Mew :-D I gots to have breakfast.

Mew

laterz

user228700

Laterz (:-P)

Secret

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