The h Bar

NeuroFuzzy

12:03 AM

@0celo7 3+13=5+11=16 wooo

ACuriousMind

Who the hell cares about primes? Number theory just bores me to death.

Damn, I didn't see that, for a change :D

0celo7

it's better that way

Mark Mitchison

@TanMath I don't know that paper in detail. However it must be the case that the population of site 3 vanishes eventually. Assuming that there is a decay process with rate $\kappa_3$ acting on that site, eventually all of the population will disappear from the system, or be trapped in the other sites.

NeuroFuzzy

he confessed his love, it was quite moving.

ACuriousMind

Is there a way to see how many messages a user has removed? That'd be an interesting statistic :P

0celo7

12:07 AM

"a user"

ACuriousMind

@NeuroFuzzy D'awwwwww

0celo7

we all know who you're referring to

ACuriousMind

@0celo7 Yep, of course I want to know how much Danu is hiding from me :P

0celo7

funnily enough, that was my thought too

that dutch sneak

I wonder how much you've hidden from me?

Like why are you always so happy when that phonon is around

TanMath

@MarkMitchison thanks.. that makes sense... Now, I originally thought the initial rho is equal to the groundstate of the hamiltonian time the dagger of that..but in literature they say that the initial excitation is on site 1.. should my initial rho be |1><1|?

ACuriousMind

12:13 AM

@0celo7 Hehe...some things should remain in the dark.

0celo7

Yeah like your ugly ass socks

NeuroFuzzy

-secret nod-

ACuriousMind

(remo

0celo7

you don't want to know

It's hideous

People always talk about it when they think he's not listening

At least a diaper covers you up

NeuroFuzzy

noooo

ACuriousMind

12:18 AM

I'll get the mind bleach.

Heya, @Danu, how's Prague?

TanMath

12:30 AM

@ACuriousMind he does nt like you!

ACuriousMind

:'(

user54412

From facebook, I just learned of a cool picture taken of Dione:

user54412

4

user54412

The thin horizontal line is Saturn's rings. The bands at the bottom are shadows of the rings on Saturn itself.

user54412

It's pretty insane how thin the rings are compared to their width.

TanMath

12:43 AM

@ACuriousMind :'(:'(:'(:'(

😭😭😭

ACuriousMind

@ChrisWhite Is the picture monochromatic, or is there another reason it's so grey?

user54412

@ACuriousMind monochromatic

user54412

that camera actually has 18 filters covering visible through near-IR, but I'm not sure they took the image in more than one filter

user54412

actually 15 filters + 1 everything-gets-through + 2 IR polarizers it turns out

user54412

or something like that -- anything NASA says tends to get all sorts of re-interpretations as the message gets passed around

0celo7

1:24 AM

@ACuriousMind that's so like you: just wipe your mind of the criticism

I did not bring enough pants to college.

ACuriousMind

@0celo7 I obviously don't know what you're talking about.

(the bleach is quite effective)

0celo7

@ACuriousMind you're lucky no one else is willing to put up with me

0celo7

1:39 AM

@ACuriousMind this deformation retract business is giving me a headache

can you help?

ACuriousMind

@0celo7 What gives you a headache about it? The intuition is that a deformation retract onto a subspace keeps the subspace fixed and continuously draws the rest of the space into it.

0celo7

let $A\subset X$, $r:X\to A$ (retract), $i:A\to X$ (inclusion), $f_t:X\to X$ (deformation retract)

user54412

@JohnRennie: Can you help here? — Feynman 7 mins ago

0celo7

then we have $ri=1_A$

this seems obvious to me

user54412

I feel bad for John Rennie sometimes. With great reputation comes great responsibility.

4

ACuriousMind

1:42 AM

@0celo7 careful!

0celo7

better?

ACuriousMind

What is that $1$ on - $A$ or $X$?

0celo7

pls I fixed it

I thought that part was obvious...

good question. I think it's not defined there?

ACuriousMind

Yep, sorry for that

Okay, onward, $ri = 1_A$. What's next?

0celo7

ok, then he says $ir\simeq 1$, where $\simeq$ means homotopic

I'm assuming that should be $1_X$

(he does not specify)

@ChrisWhite but you don't feel sorry for ACM?

I'm not sure how to prove this

I drew a picture, but the picture is confused

ACuriousMind

1:45 AM

@0celo7 Yep, it's $1_X$.

What do you mean, prove?

0celo7

I have no intuitive notion of what $\simeq$ means

ACuriousMind

From which givens do you want to prove it?

0celo7

He defined $a\simeq b$ if there is an interpolating $f_t$

I want to show that $f_t$ interpolates between $ir$ and $1_X$, thereby establishing $\simeq$

ACuriousMind

@0celo7 It means you can continuously deform the l.h.s. into the r.h.s. Formally, I find it easiest to say that $f: X\to Y$ is homotopic to $g : X\to Y$ if there is a continuous map $F : X\times[0,1]\to Y$ with $F(\dot{},0) = f$ and $F(\dot{},1) = g$.

0celo7

@ACuriousMind way to restate exactly what I said and what the book says...

I'm not sure what "continuously deforming $ir$ into $1_X$" means though

ACuriousMind

1:49 AM

Have you seen examples?

0celo7

nay

I want examples!

ACuriousMind

Okay!

user54412

What definition of "deformation retract" do you have that doesn't just get you the answer. (Or are you not assuming $f_t$ is a def. ret.?)

ACuriousMind

^also, that

0celo7

I don't see how $f_t$ comes into play here at all

well maybe I do

I would appreciate an example

ACuriousMind

1:51 AM

Example: Take the interval $[0,1]$. Then $F(x,t) = t + (1-t)x$ is a deformation retract onto the right endpoint $1$.

0celo7

yes

ACuriousMind

Example: Take the plane $\mathbb{R}^2$. Then $F((x,y),t) = (x,(1-t)y)$ is a deformation retract onto the x-axis.

0celo7

so $r:[0,1]\to \{1\}$

@ACuriousMind that was not the part I am confused about

I am confused about how $ir$ is homotopic to $1_X$

ACuriousMind

Well, take my first example: $r$ is the constant map that's just $1$. $i$ is the map that's $1$ at $1$, so the map $ir$ is just the constant map that's 1. We have $F(x,1) = 1$, so $F(\dot{},1) = ir$. Also, $F(\dot{},0) = 1_X$, and $F$ is continuous in $t$, so $F$ is a homotopy between $ir$ and $1_X$.

0celo7

I see

aaaaaaaahhhhh

moving on

ACuriousMind

1:59 AM

I still don't know what you were confused about, but if you aren't anymore, good! ;)

0celo7

I was confused about math

durr

@obe got any QM/RG questions?

or just chillin here

@ACuriousMind what is the $\epsilon$-neighborhood of a space?

ACuriousMind

@0celo7 Of a subspace of a space?

0celo7

@ACuriousMind are you familiar with the example: house with two rooms

@ACuriousMind yes, I'm assuming it's like a ball around the subspace w. radius $\epsilon$?

ACuriousMind

@0celo7 Exactly, only it's not a ball

And no, I'm not familiar with the house with two rooms

0celo7

@ACuriousMind not a ball?

obe

2:10 AM

@0celo7 afk, reading qm. (playing sc2)

ACuriousMind

@0celo7 No, it's just the set of all points that have less than $\epsilon$ distance to the subspace. If the original subspace wasn't a ball, this isn't, either.

0celo7

@ACuriousMind cf. that picture, but I need to figure out this nbd business first

@ACuriousMind well is it homotopic to a ball?

ACuriousMind

@0celo7 Only if the subspace is homotopic to a ball

0celo7

funnily enough this one is

but that's the point of the proof

he says that the closed $\epsilon$-nbd $N(X)$ of $X$ will deformation retract onto $X$ if $\epsilon$ is sufficiently small

why does the size of $\epsilon$ matter?

so that parts of $N(X)$ do not "double up" or something?

user54412

Suppose X is a disconnected subspace of R^2 (2 disjoint filled-in circles, to be concrete)

ACuriousMind

2:14 AM

@0celo7 There could be a hole in the way: think of an annulus, and an $\epsilon$-neighbourhood of a point close to the inner border - for large $\epsilon$, the neighbourhood will contain the hole, and you can't deformation retract it to the point.

0celo7

@ACuriousMind because it's no longer simply connected

OK, but what about in this case? Here we're talking about the nbd of the whole of $X$

ACuriousMind

Indeed. Chris' example is stronger, there the neighbourhood is not even connected.

0celo7

yes but what about this space

or is he saying that this is a condition in general

user54412

@ACuriousMind Actually, I meant to illustrate that with large enough $\epsilon$ the neighborhood changes topologically by becoming connected.

user54412

I think we can forgive 0celo7's use of "ball" -- it's an understandable generalization of the word.

user54412

2:22 AM

@0celo7 Which space exactly?

ACuriousMind

@0celo7 I don't think that's a general condition, the Hawaiian earrings should be a counterexample.

Being a metric space does not mean small enough neighbourhoods become simply connected.

0celo7

I mean something homotopic to a ball

math.cornell.edu/~hatcher/AT/AT.pdf

page 13 of the pdf

ACuriousMind

@0celo7 I think by "clearly" he's telling you to just let your intution tell you that works - Just "thicken" all the surfaces X consists of a bit - that's a neighbourhood and retracts back into X without problems.

0celo7

well that's what I did

but why "sufficiently small"?

if $\epsilon$ becomes too large, does crazy stuff happen?

ACuriousMind

Well, make it so thick that the tunnels are filled in. Is it still obvious to you that this retracts? (If yes, his following argument how it is homotopic to the unit ball becomes completely superfluous)

0celo7

2:29 AM

@ACuriousMind that's what I meant by "double up" above

obe

@ACuriousMind I failed, I'm only in silver and I had a 7 lose streak right now.

user54412

sketchesoftopology.wordpress.com/2010/06/23/…

ACuriousMind

@0celo7 Well, then you understood it! (Without seeing Hatcher's argument, I couldn't tell this was the point)

0celo7

@ChrisWhite I can't tell what's going on there :/

@ACuriousMind well this whole thing seemed rather obvious to me

so I'm confused by being confused

?

user54412

It's just the deformation retract to a point, but done in the language of complexes (cf. page 14 of Hatcher).

0celo7

2:34 AM

@ChrisWhite I see

alright, that's enough for tonight

I need to sleep on that

@ACuriousMind if you're not home, may I ask where you are

ACuriousMind

@0celo7 Sitting friends' cat :D

@0celo7 Sometimes, things that seem obvious just are obvious ;)

obe

2:52 AM

I need to re-learn QM when I'm finished. Would Sakurai be the best option?

@ACuriousMind Have you read the long book by Cohen on QM (2 volumes)?

ca.wiley.com/WileyCDA/WileyTitle/productCd-047116433X.html

ACuriousMind

@obe Nope. Never read a QM book.

obe

I forgot, your lecturers must be really awesome.

0celo7

My school uses samurai

Damn autocorrect

ACuriousMind

Nice autocorrect :D

0celo7

@obe my neighbor in VA the quantum Chem prof loves Cohen Tannoudgi

Or however you spell it

obe

2:57 AM

It's an undergraduate text though?

0celo7

She used it during grad school at Upenn

obe

Do you like it?

0celo7

Never opened it

Physics Meta

0

Q: Is this a good question? - How come Land Speed Records for Cars get higher speeds than motorcycles? (Even though they're less aerodynamic?)

Is this a good question? How come Land Speed Records for Cars get higher speeds than motorcycles? (Even though they're less aerodynamic?) Is it because more rocket can be packed onto a car, as compared to a motorbike?

discussion

dmckee

4:15 AM

@obe Neither a good introductory text, nor a good reference. Not a bad text for a second look, however.

DanielSank

4:51 AM

@TanMath I wanted to talk to you about your question. I think you're just taking the slope of the data too seriously. Obviously it will not keep rising like that forever.

TanMath

5:38 AM

@DanielSank yeah, but without the reaction center in the model, where will the excitons go?

DanielSank

5:59 AM

@TanMath I have no idea.

Mark Mitchison

6:33 AM

@TanMath Yes, the initial rho should be |1><1| if the excitation is initially localised on site 1.

@TanMath If there is no reaction centre (i.e. no loss mechanism on site 3) then the excitons will just be transferred between sites in endless Rabi oscillations, assuming there are no other dissipative processes. If there are dissipative or dephasing processes then the populations of the excitons on each site will reach some steady state which will depend in a complicated way on all the relevant energies and rates.

yuggib

7:23 AM

:23569703

cohen is a good book, with a modern notation. If else Messiah is a bit old but nice

but for understanding the third volume of Landau (the one on QM) in my opinion is the best by far.

Danu

10:11 AM

@ACuriousMind Puh-rrrretty good!

Consequently, I'm puh-rrretty hung over right now.

skull patrol

Hi pal :-)

hangover

PSY - HANGOVER feat. Snoop Dogg M/V

►

0celo7

11:09 AM

So I'm pretty sure my roommate talks in his sleep

0celo7

12:50 PM

@skullpatrol I've never seen this, didn't miss much

0celo7

1:58 PM

@ACuriousMind The lin alg TA was impressed I know about K theory and Atiyah Singer...

I guess he's never heard about freshmen taking Alg Geom

@ACuriousMind what are the rereqs for QoGS again?

ACuriousMind

@0celo7 Show-off :P (Why would you begin to talk to a LA assistant about K theory, anyway?)

0celo7

@ACuriousMind uh because he's a topologist

i asked him about books

ACuriousMind

@0celo7 Canonical quantization in QM and QFT, Hamiltonian mechanics, enough algebra to feel comfortable with graded algebras and homological resolutions, helps if you've seen Grassmann variables before.

0celo7

cohomology?

TA said he used link.springer.com/book/10.1007%2F978-1-4684-0627-6 for index theorems

He said I need some functional analysis first

ACuriousMind

It helps if you've seen (co)homology before, but they don't take the full-on mathematical approach to do it by Lie algebra cohomology, they stay quite physical by considering "enlarging the phase space" instead

QoGS has nothing to do with index theorems, by the way

0celo7

2:12 PM

I know

I'm just interested in them

ACuriousMind

Yeah, you need a bunch of functional analysis for that, since it concerns Fredholm operators and such things

I guarantee that about 95% of working physicists just believe the index theorem, though :D

0celo7

95% of engineers just believe the physicists

I've seen some of the shady shit you do

I won't be one of them

Aug 16 at 17:39, by Slereah

there are few things more powerful mathematically than physicist bullshit

@ACuriousMind so I need to talk to the functional analysis people?

I want a very gentle intro

ACuriousMind

Well, you need a solid foundation in finite-dimensional analysis as well as finite-dimensional linear algebra to do functional analysis, I'd say

0celo7

so I need to do real analysis

I have to face the enemy?

ACuriousMind

Well, if you stay clear of the main examples ($L^p$ spaces), you might not need much analysis, but convergence of series and such will definitely show up. Come to think of it, topology of metric spaces and such is perhaps more appropriate for an "abstract" course of functional analysis on Banach spaces, but it'll depend on the approach you take, I'd say.

0celo7

2:28 PM

shame you don't know books

the grad students here have lists of them memorized

*seem to

no clue if they actually do

FenderLesPaul

2:45 PM

@0celo7 off the top of my head: Schutz, Hartle, Wald, HE, Straumann, Poisson, Carroll, and Padmanabhan I would say

0celo7

>forgetting the greatest one

you call yourself a...what do you call yourself?

FenderLesPaul

a spongebob enthusiast

0celo7

Gravitation & Cosmology

FenderLesPaul

You take that back sir

0celo7

can't take back the truth

also where is De Felice & Clarke

we were talking about it yesterday or the day before

FenderLesPaul

2:48 PM

I've only gone through like 4 chapters of that book though

0celo7

I get the feeling that I overdid it and now ACM will never read Straumann :(

ACuriousMind

3:15 PM

I'm voting to close this question as off-topic because it is about the religious implications of electrolysis. — John Rennie 11 mins ago

...and @KyleKanos sent OP to christianity.SE :O

FenderLesPaul

@0celo7 it's all your fault!

obe

@ACuriousMind lol

0celo7

@ACuriousMind Am I right?

ACuriousMind

@0celo7 Well, no, I have not actively decided to not read Straumann.

0celo7

@ACuriousMind lol

Haha Lubos answered!

ACuriousMind

3:28 PM

He seems bored today, he's written several wordy answers.

0celo7

...and he calls special relativity problems that are not obvious to me " basic high school problem in classical physics"

-.-

FenderLesPaul

3:50 PM

what the actual fuck?

-9

Q: Would it be a sin?

Well, for example, we have holy water. That is H20. If we decompose it by electrolysis into components, then we get a holy Hydrogen and Oxygen? If yes, then is it possible to get by nuclear fusion holy Plutonium and make holy atomic bomb? And if we'll destroy someone by this, whether it be a sin,...

nuclear-physics

the answer is nuts in a really funny way haha

obe

4:03 PM

and... he has more rep than me!

(for that question only)

ACuriousMind

@obe No, it's the association bonus

obe

Ok.

ACuriousMind

(because the user has >200 on SO, they haven't earned that rep on physics

Someone voted that question up, though. And btw, voting up joke answers is also not really good because it blocks the automated deletion routine.

0celo7

@obe yes, that user is objectively better than you

yay, new keyboard is downstairs

ACuriousMind

Remember, "we hate fun"

obe

4:05 PM

Remember Blah had more rep than me by commenting Blah, Blah, Blah?

0celo7

@ACuriousMind wait, voting up an answer blocks the deletion of the question?

ACuriousMind

@0celo7 Yes, questions with positive score answers are not cleaned up by the roomba

0celo7

> Will this mouse pad work with my mac?

obe

Who said this?

0celo7

amazon.com/forum/-/Tx27RLRUTP9LWSC/…

> This perfectly demonstrates the intelligence of Mac users.

wow random Amazon people think I'm dumb

ACuriousMind

4:11 PM

9

Q: What would happen if Superman was bitten by a vampire?

Does being bit by a vampire affect Superman? If yes, how, and to what extent? If no, then why?

superman vampire

The real questions. :D

0celo7

@ACuriousMind I was unaware of this. I apologize for my +1

> He was in fact was once bitten by Dracula. But because the Man of Steel is fueled by the sun, Dracula immediately exploded.

ACuriousMind

That's not a joke answer, by the way :D

0celo7

Christianity SE is very pretty.

@ACuriousMind When are we going to get a better font so TeX blends better and the new layout?

ACuriousMind

Six to eight weeks.

0celo7

When did they say that?

Also why so vague? What's so hard about hitting a button and switching everything over?

HDE 226868

4:20 PM

376

A: The Many Memes of Meta

Meme: 6 to 8 Weeks Originator: Jeff Atwood First Heard: May 13th, 2008 Cultural Height: In about 6 to 8 weeks Definition: The time estimate given "off the top of my head" when the Stack Overflow team has only a vague idea of how long a task will take because they have little-to-no formal sche...

ACuriousMind

^that :)

FenderLesPaul

Damn

all the undergrads are coming back today

0celo7

you're an undergrad...

also I'm an undergrad

FenderLesPaul

no one needs to know that :p

I just like how empty and quiet it is during the summer

0celo7

TA Holloway asked me "are you an undergrad"

FenderLesPaul

4:22 PM

during the year it's just cluttered with people

0celo7

please your campus is half the size of mine

0

A: Does ice melt slower in space?

Yes in space its vacuum means no pressure ano air no gravity and as u said ice melts fastly in high pressure so in space ice will take long to melt if its not so hot thre 😋

kill it with fire

obe

Well, does it? ;P

0celo7

not sure, that would require me to know 1st year physics

obe

That person made an account just to write that answer.

0celo7

@obe (1) you're playing SC (2) you're writing answers (3) you're not doing QM

FenderLesPaul

4:25 PM

I have to start tutoring again

0celo7

pick one, wisely

FenderLesPaul

the things I have to do for money :(

I'm pretty accepting and understanding of different backgrounds of different people from engineers to pre-meds

0celo7

oh god the kerning

FenderLesPaul

but I can't tell you how many times I had an engineer in the EM for engineers class

0celo7

@ACuriousMind why did you do this to me

FenderLesPaul

4:26 PM

ask me how to do integral of x^2

0celo7

@FenderLesPaul ooh, I got this one

you bring down the $2$

add $1$

then maybe increase it?

and then a +C!

FenderLesPaul

sure why not

ACuriousMind

@0celo7 bwahahahaha... 'cause I'm evil

0celo7

you're telling me only engineers don't know how to do integrals

that seems BS

I can do integrals, and by no true scotsman all real engineers can do integrals

FenderLesPaul

it' an EM for engineers class

0celo7

4:29 PM

QED bitch

obe

@0celo7 (5)

0celo7

I'm going to take EM for engineers

your point?

FenderLesPaul

my point is I have kids in that class not knowing how to do integral x^2

0celo7

oh are you saying you tutor that class specifically?

FenderLesPaul

I never said only engineers don't know how to do integrals

0celo7

4:30 PM

okok

that reminds me, I have to do some integrals for ODE

obe

Is it honors ode?

0celo7

also start Hatcher 4real

@obe yes

also start analysis 4real

also continue Weinberg

obe

I have to finish QM in 10 days.

or else I will die.

0celo7

10?

how did you go from 30 to 10 in less than 20?

counts fingers

obe

I want to finish earlier.

I need to also read some sections in sakuraii.

That I missed in this book.

0celo7

4:33 PM

am I the only one who thinks QM in 10 days is completely ridiculous

it would take you 10 days to do the exercises

obe

Depends on book.

Shankar obv.

0celo7

@ACuriousMind do you think you could cram a semester of anything in 10 days?

and be able to do exercises within the material

ACuriousMind

@0celo7 Newtonian mechanics, perhaps :D But no, not really

Digital Trauma

Hi @HDE226868, If you don't mind, I'd still like some clarification for this edit reject reason

FenderLesPaul

10 days for QM?

damn

there's a reason most colleges have like a year to teach QM lol

and then another year to teach QFT

obe

4:39 PM

It suffices for a mediocre understanding enough to do basic qft.

I'll re-learn later.

HDE 226868

@DigitalTrauma Ah, right. Well, I, too, use "blade" instead of "leaf", but the replacement is akin to replacing "lorry" with "truck". It's minor and probably won't make much of a difference.

FenderLesPaul

@obe does it?

maybe you're underestimating how hard QFT can be

it's significantly harder than GR for example

in my opinion anyways

obe

whatever we'll see how it happens.

FenderLesPaul

alrighty

0celo7

@ACuriousMind really? :( I thought the later problems were tough

FenderLesPaul

4:43 PM

you got time anyways

Digital Trauma

@HDE226868 Lorry vs truck is different - these are regional differences and both perfectly accurate and common in their native locales. IMO fan leaf is completely odd, unusual usage in any context (I think we're supposed to default to US English here)

0celo7

this keyboard is bigger than my laptop

HDE 226868

@DigitalTrauma "Leaf" was used in the question, too, so consistency is probably better. As it is, the edit to the question completely nullifies that reason, so if you propose the edit again, I'll approve it.

ACuriousMind

@DigitalTrauma Just as an explanation: In German, the "blades" are called Blätter, of which the literal translation is leaves. Perhaps the Czech word is similar, this would explain Lubos' (and the asker's) odd usage.

@0celo7 No idea what you mean by "later problems".

Also, that wasn't meant 100% serious. I have no idea how long it would take me to do exercises competently.

0celo7

@ACuriousMind just more complicated ones

HDE 226868

4:50 PM

@DigitalTrauma I still don't think that it improves readability much, though.

Digital Trauma

@ACuriousMind Yes, I'm definitely not blaming Lubos' (and the asker's) non-native usage here. I'm very happy that SE is open to all AND that the edit facility allows good answers to b made more accessible

TanMath

@MarkMitchison well, there is dephasing in the model..

0celo7

@Huy this is awesome

TanMath

@MarkMitchison you said that it will decrease to a steady state.. so how will the infinite integral of the site 3 population converge if this steady state is not equal to 0?

Digital Trauma

@HDE226868 I'm glad the unusual usage didn't interrupt your reading. However I assume the upvotes for my comment were from people who did think it was useful. I think I'll go ahead and re-edit...

HDE 226868

4:59 PM

@DigitalTrauma By the way, since I hadn't commented on that post, I wasn't alerted by your comment. Thanks for going to chat with it.

Digital Trauma

@HDE226868 Ah - thats good to know. As you probably realised, I was assuming the @-notification would work for edit reviewers as well, but now I know thats not the case - Thanks!

HDE 226868

@DigitalTrauma No prob. Thank goodness for chat. It sounds like a good feature request though, notifying reviewers.

@DigitalTrauma Edit approved.

Digital Trauma

@HDE226868 Yes.

@HDE226868 Thanks! If this edit ends up being rejected, I promise I'll shut up and not bang on about this any more ;-)

ACuriousMind

@DigitalTrauma Approved it, you can rest easy ;)

Digital Trauma

@ACuriousMind Thanks! I'll leave my comments up for a bit in case there are more questions, but I'll clean them up in a day or two

HDE 226868

5:22 PM

Ah, good, problem solved.

bolbteppa

If I give you a Lie algebra and form it's universal enveloping algebra, is it the analogue of complexifying that lie algebra and then finding it's twisted universal enveloping algebra?

Huy

@0celo7 What is?

ACuriousMind

5:42 PM

@bolbteppa Is proposition 1.6.4 here what you mean?

It essentially says it doesn't matter whether you twist and them form the UEA, or complexify, form the twisted UEA, and then divide out the complex part again.

bolbteppa

Awesome, I hadn't seen that theorem and I cannot even understand how you got that intuition from the statement (but I like your intuition!), I'm motivated by the statement that "In a completely similar fashion we can obtain the Dirac operator as a twisted Casimir operator for the complexified Poincare Lie algebra" www1.mat.uniroma1.it/people/fiorenza/giuseppe-final.pdf

Mark Mitchison

@TanMath @TanMath The steady state will be equal to zero, since there is a process that extracts population from the system with rate $\kappa_3$ (I am assuming, you didn't actually state that in your question). There is a possibility that the steady state is not 0, if some population is trapped on sites that are not connected to site 3 by the Hamiltonian. However, I doubt this is the case in your model

TanMath

5:58 PM

@MarkMitchison thanks, I ask because with some of the simulations, it converges to 1/7, not zero...

Mark Mitchison

@TanMath If there is a constant decay process acting on that site, then the population should converge to zero.

I don't see how any other outcome could be possible.

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