The h Bar

Semiclassical

15:00

nonlinearity is both a blessing and a curse

it means you can have all these interesting solutions, but you have to get rid of superposition to do that

and that suuucks

Sid

@Kaumudi.H Things are good (where things!=Professors). How about you?

0celo7

@Semiclassical all of the good equations are nonlinear

CooperCape

Someone told me cylinders aren't curved because you can parallel transport vectors on them without them changing direction... is this a legit thing?

0celo7

but the Yamabe equation is especially nasty because the power in the exponent leads to a bad term (functional analytically speaking) in the Lagrangian

Semiclassical

@CooperCape yeah. compare the cylinder to the sphere: with the sphere, if you take two cross-sections (intersections with a given plane) then both of the resulting figures will be curved.

CooperCape

15:05

okay...

Semiclassical

by contrast, with the cylinder you can take one of those cross-sections to be along the axis of the cylinder and therefore straight

so it's only curved in one direction, whereas the sphere is curved in any two directions

as a consequence, the cylinder has zero Gaussian curvature whereas the sphere doesn't

CooperCape

Ahhhh okay

Balarka Sen

Physical chemistry is kinda cool, tbh

CooperCape

yeah but organic chemistry is uhh... hmmm..

Semiclassical

p-chem is mostly stat mech + thermo

and therefore is pretty cool

Balarka Sen

15:08

Organic chemistry on the other hand is a scum on the face of the earth

Semiclassical

lol

Anonymous

@BalarkaSen I'm offended :P

Semiclassical

^ /triggered

Anonymous

I love organic chemistry

Balarka Sen

what is offense? baby don't flag me

no more

Anonymous

15:09

lol

Anonymous

loo

Anonymous

lemme flag...XD

Sid

@BalarkaSen That is a very wrong description.

Anonymous

tbh...I like everything other than history, geography, vernacular and sociology probably

Semiclassical

I'm forgetting what stuff's in p-chem beyond thermal physics + stat mech tbh

Anonymous

15:12

@Semiclassical chemical/ionic equilibrium stuff, electrochemistry, etc

CooperCape

Equilibria?

Semiclassical

hmm, okay

though i'd count chemical equillibrium as stat-mech

Balarka Sen

I thought so

Anonymous

@Semiclassical Yes, that's possible

CooperCape

pH...

Anonymous

15:14

@CooperCape that's ionic

Sid

Kinetics, Moles and stuff...

Semiclassical

I guess that's the point, though

Anonymous

mole concept is just arithmetic

Semiclassical

physical chemistry

Anonymous

kinetics is stat-mech

Anonymous

15:14

rest of chemistry is quantum mechanics in the background

Semiclassical

and electrochemistry is pretty stat-mech as well

Sid

@Blue Well, yes. But, just put in some chemical equations and it becomes Chemistry! :P

Semiclassical

one thing which I know shows up in p-chem sometimes, though, are point symmetry groups

Anonymous

@Sid Chemists would be offended if they saw us trivializing their field (Well, mathematicians do it to us all the time :P)

Semiclassical

and you don't always see that in physics

Balarka Sen

15:16

I'm reading solutions stuff/kinetics/electrochemistry and I kinda love it

kinetics is all about ODE's man

A chemical equation gives a system of ODE's by taking the various rate equations

Semiclassical

reminds me of the first project I did under my advisor

take your system to be a narrow channel connecting two reservoirs

0celo7

ODEs are scum

it's engineering math

Balarka Sen

no u

nasil

If the higgs boson has mass than it means that it also interacts with another higgs boson and also that one should too so it goes on and on. Are there infinetly many higgs bosons around us?

Semiclassical

narrow enough that particles inside the channel can't move past one another

0celo7

15:18

"Humidity 100%"

wtf

shorts and t-shirt weather in November

Balarka Sen

ODEs are amazing

they are the gateway to dynamics

Semiclassical

and the material surrounding the channel being sufficiently insulating that the electric field lines of any ions are trapped inside the channel

then Gauss's law tells you that the electric field along the channel between any two charges will be constant

and therefore you have a logarithmetic interaction potential

which leads to blah blah blah blah

Sid

@0celo7 What on earth? Do you want to catch a cold or something?

0celo7

@Sid it's hot as balls out there

Anonymous

I think he means it's hot and humid there

0celo7

15:20

and humid af

Sid

@0celo7 Temperature?

0celo7

70

Anonymous

farenheit

Anonymous

*units

Semiclassical

here it's 27 F and 70% humidity

0celo7

15:21

What other unit would I use?

Semiclassical

so definitely coat weather

0celo7

@Semiclassical lmao

Anonymous

@0celo7 Kelvin

Semiclassical

not heavy coat weather, though

save that for the teens

0celo7

@Blue if it were 70K here, you'd feel it too.

Anonymous

15:22

@0celo7 Well, you could be sitting in some underground fridge chamber :P

Semiclassical

my 'joke' for why I like Fahrenheit in everyday life despite preferring celsius/kelvin for scientific considerations

Sid

@0celo7 That's not hot. That's blanket weather...

Anonymous

21 C....that's the coldest we get around here

Anonymous

It's pretty cold

Semiclassical

0 C and 100 C respectively define the freezing and boiling points of liquid water

by contrast, 0 F and 100 F respectively define my freezing and boiling points

Sid

15:24

22 C here and I am wearing a sweater and wrapped in a blanket...

Semiclassical

@Blue It's -3 C here right now

soooo

0celo7

You're Indian

I'm German

my people die in the summer. literally.

Anonymous

@Semiclassical We're of different breeds. I'm heat tolerant. You're cold-tolerant

Semiclassical

yeah, that's pretty true

Balarka Sen

It's -10C and I'm feeling mildly warm

I'm Russian

Sid

15:25

@BalarkaSen You're a polar bear

Semiclassical

though Minnesotan attitudes towards winter depend on the time of year

0celo7

@BalarkaSen Seriously, are you the reincarnation of a Soviet mathematician?

is Buddhism real?

Balarka Sen

@Sid Nah, I'm just in the middle of Siberia

Semiclassical

when winter is just about to start, we have our own "dammit winter" moments

but once it's settled in we're like "eh, not so bad"

though if it gets to 0F then my brain does start to go a bit winter-crazy

Balarka Sen

@0celo7 I am the very model of a Russian mathematician

That's a meme, but no

Semiclassical

15:27

and then there's that point in the beginning of the year when winter just won't end g**-d*****

0celo7

according to the phone, it's done raining for the day

do I trust the phone?

Anonymous

It's apple. So, no

0celo7

@Semiclassical yesterday I discovered that doing A=k for an array A and a real k just sets every entry to that

that's actually pretty nice

bolbteppa

Chemical equilbrium is stat mech, amazing how deep you need to go to justify that stuff

Semiclassical

Fortran?

bolbteppa

15:30

Law of mass action in full glory is no joke

0celo7

@Semiclassical ya

Semiclassical

kk

Transport theory via the Boltzmann equation

that's a hell which I have no intention of entering

bolbteppa

Just too much work to do to even set it up properly

Semiclassical

admittedly it does lead to some interesting stuff

Cluster diagrams for the virial expansion etc

there's a lot of commonality with QFT, which isn't surprising insofar as both are dealing with many-body systems

bolbteppa

Getting closer to stat mech in biology crcpress.com/Physical-Biology-of-the-Cell/…

@Blue well, kinetics is more-so non-equilibrium stat mech which hasn't been properly formulated from a QM perspective, while the rest of chem is equilibrium stat mech (for multi-particle systems) or QM (for few-particle systems)

Anonymous

15:48

Ah, right it's indeed non-equilibrium stat-mech

bolbteppa

Even the equilibrium formulation has all sorts of issues if you look under the surface

Anonymous

multi-particle systems are at the junction of stat-mech and qm tbh

bolbteppa

Yeah but the difference is that in stat mech you set up a simpler distribution function rather than the full-on density matrix which encapsulates the additive symmetries of your systems

Anonymous

I was looking for good books on the many-body problem. Any suggestion? I'd like to read it after my exams, in december. Heard this (amazon.in/Feynman-Diagrams-Many-body-Problem-Physics/dp/…) is good

bolbteppa

The Fetter-Walecka book on that page is recommended a lot

Anonymous

15:51

@bolbteppa What are the pre-requisites ?

Anonymous

amazon.com/Quantum-Theory-Many-Particle-Systems-Physics/dp/…

Anonymous

found it

bolbteppa

Gotta be honest I don't understand that stuff at all

Anonymous

I'm supposed to work on that stuff next summer vacation

Anonymous

I feel like I know nothing

Anonymous

15:53

Haven't even completed qm properly

Semiclassical

I like Altland and Simons for this stuff

cambridge.org/gb/academic/subjects/physics/…

Anonymous

@Semiclassical Oh, my professor also mentioned that. It looks a bit math-intensive but I should try reading it

bolbteppa

My sense is that the two bible books in this area are amazon.in/Methods-Quantum-Theory-Statistical-Physics/dp/… and amazon.com/Statistical-Physics-Part-Theory-Condensed/dp/… along with Altland and Walecka but I genuinely have no idea what's going on here or why you need it or want it at the moment

Anonymous

Thanks for the suggestions @bolbteppa @Semiclassical

John Rennie

@Dvij The temperature is measured by an observer stationary at infinity

DanielSank

16:06

@heather this may be useful to you

0

Q: Extract single qubit state from combined state in QuTiP

I would like to extract the state of single qubits from combined states, using QuTip (the Quantum Toolbox in Python. Is there some QuTiP function that will extract a single qubit state from a combined state? Example For example, suppose I begin with two qubits, $|0\rangle$ and $|1\rangle$. I c...

0celo7

@Semiclassical oh my god the next homework is another shooting method

Slereah

How very American

Just shoot at your problems

0celo7

“Epsilon_0 infinitely small with respect to rho”

How very precise

Balarka Sen

I think this is enough chemistry for today.

This is fine

John Rennie

@CooperCape the surface of a cylinder is flat in the sense that it has no intrinsic curvature. If you unroll the surface off the cylinder you get a flat sheet.

Balarka Sen

16:35

You can draw the parallel transport on the cone to see that it has curvature, in contrast

I recommend trying it

The new Vsauce video does a pretty good job explaining curvature, but imo it can be done a bit better.

0celo7

Curvature is the obstruction to the local Euclidean isometry equation being integrable

Anything else is garbage and unhelpful

Balarka Sen

ur garbage and unhelpful

But yes it is the obstruction to being isometric to R^n locally

0celo7

I know it is

Did you do the exercise in do Carmo that asks for that?

Balarka Sen

Ya

0celo7

I swear to god my phone sends messages without me hitting return

bolbteppa

16:48

How does that definition/idea apply to the definition of curvature $y''/(1+y'^2)^{3/2}$ of $y = f(x)$.

Balarka Sen

That's curvature of a curve, which is an extrinsic idea.

But two curves in $\Bbb R^3$ are congruent iff they have the same curvature and torsion coming from their TNB frames

So it is an obstruction to flatness of the embedding $[0, 1] \to \Bbb R^3$ of sort

Sir Cumference

17:34

@0celo7 Quick question

You can't add numbers of different dimensions, right? E.g. adding 5 m/s with 7 Joules is meaningless

Anonymous

@SirCumference I had seen your question earlier today. The definition "multiplication is repeated addition" is a short-sighted one.

Sir Cumference

Right, I thought about it for more than half a second and realized the problem

Slereah

It is well defined on the integers

and that's the basis of all multiplication

Sir Cumference

@Slereah Natural numbers, at least, follow that definition

Back in Calc I remember when we learned about series and partial sums, the first thing on my mind was "if integration can change the dimension of a function, can a partial sum change the dimension of a sequence?"

Really, I never understood how to think of combining numbers with different dimensions

Phase

17:52

What's the difference between $e^a$ and $e_a$, and the difference between say, $d^a_b$ and $d^{ab}$ or $d_{ab}$?

0celo7

@SirCumference I mean, you can make it make sense.

For example, consider the group $U$ of all units.

Then there is the "group algebra" $\Bbb RU$ which contains formal linear combinations of group elements over $\Bbb R$.

In that sense $5m/s+7J$ is perfectly valid.

Nonsensical, but defined.

Anonymous

@0celo7 His original question was why multiplication of units is not repeated addition: Like $1 N \times 1 m = 1 Nm$ (work/energy). According to him it doesn't make sense because "repeated addition" of $m$, shouldn't produce $Nm$.

0celo7

That's how multiplication in $\Bbb N$ works, but not in abstract groups.

inb4 Balarka says some smartass heckcrap

Anonymous

BTW $N$ here stands for the unit of force Newton and $m$ stands for the unit of length.

Anonymous

I'm sure multiplication of dimensions/units has some formal definition

Anonymous

18:03

It's more like "composition" of units

0celo7

it's just a group structure

Balarka Sen

units are neither normal nor formal

Akiva Weinberger

18:47

@0celo7 You changed your icon

(from this thingy:)

Well, a better-looking version of it anyway

Here's a hint on how to deform it to a double torus minus a disk

I think this was your icon at the time?

0celo7

have you been obsessing over this the whole time :P

Akiva Weinberger

No I just remembered it now

and I remembered I still had the link

But now I'm actually a bit confused

Semiclassical

@0celo7 Lol, what’s the ODE this time?

Akiva Weinberger

Is that the same surface?

It looks like it's dodecagons instead of hexagons

Semiclassical

The nice thing about the Mathematica code for the last one is that you can probably adapt it for this one

Anonymous

18:57

@Semiclassical halp

Anonymous

I'm trying to prove $$C_p-C_v=[\left(\frac{\partial U}{\partial V}\right)_T+P] \left (\frac{\partial V}{\partial T}\right )_P$$

Anonymous

I thought maxwell's relations might work

Anonymous

But it doesn't seem to (at least directly)

Anonymous

I'm supposed to start from first law of thermo

Anonymous

So say I take an isobaric process...

Anonymous

18:59

$dQ=dU+dW$

Anonymous

$nC_pdT-nC_vdT=dW$

Anonymous

That right side thingy should come out to be $dW/ndT$

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