The h Bar

9:43 AM

@JohnRennie @ACuriousMind How light carry information? the question I googled some of the replies are using the photon and each photon has it own frequency and there are billions of photons that carried in single em wave

then again a different answer using amplitude and frequency modulation

which use Em wave as single entity and change in frequency and polarization carries a information

if the recieve is my eye

how our eye or brain or retina comprehend these billions of photon? or these modulated EM wave

ACuriousMind

@JackRod 1. As I've said before, please don't directly ping me with general physics questions - I hang around in chat a lot anyway and will answer questions that interest me without being pinged. 2. What do you mean by "information" here? Do you mean the information a radio signal carries or something else?

Jack Rod

yes like phone call or radio communication

ACuriousMind

in that case you found the answer already: it's amplitude or frequency modulation (on radios you might see sometimes an AM/FM switch changing between the two modes)

there is no meaningful way in which any individual photon carries that information - the information is a property of the full, classical EM wave, much like the information a book carries is not in any meaningful way carried by the individual fibers of its pages

Jack Rod

but how these modulation converted into our

language

ACuriousMind

well, our spoken words are also just waves (sound waves in air) right?

Jack Rod

9:51 AM

like If some body want to say Hi over phone ,how frequency modulation as u said be adjusted to make the Em wave carry the same information

ACuriousMind

Wiki has a neat gif on how you modulate the signal (that's the sound wave in this example!) onto a carrier wave in either AM or FM

if you know the base frequency and amplitude of your carrier wave, you can always reconstruct the signal from the A/F-modulated wave

Jack Rod

ok

can u give some idea about spectrum

efficency

ACuriousMind

I don't know what you mean

Jack Rod

Spectral efficiency

Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is utilized by the physical layer protocol, and sometimes by the medium access control (the channel access protocol). == Link spectral efficiency == The link spectral efficiency of a digital communication system is measured in bit/s/Hz, or, less frequently but unambiguously, in (bit/s)/Hz. It is the net bit rate (useful information rate excluding err...

ACuriousMind

That's about digital communication (not analog radio signals!); what exactly do you want to know about it?

Jack Rod

10:02 AM

how some frequency band are fast

while other carry the information slow like 5g is now real time network we can say

ACuriousMind

it's not a property of the frequency band as such

Jack Rod

although the speed of em wave is same

ACuriousMind

it's a property of the technology you're using to send information over that frequency band

@JackRod the speed here isn't about how quickly the wave gets from one point to the other

it's about how long it takes you to send 1 bit of information, i.e. how efficiently you can encode information with the technology you're using

Jack Rod

tech u are referring to..?

ACuriousMind

a silly example would be a technology that encodes 0 or 1 bits by sending the audio of someone shouting "One" or "Zero" - in that case your bitrate is limited by the duration of these audio clips (e.g. if both are about 2 seconds long, you can only send 1 bit every 2 seconds)

Jack Rod

10:08 AM

ok so how spectrum band affect

it mean like for 5g 700mhz is ideal ?

ACuriousMind

I'm not sure what you mean

Jack Rod

nokia.com/networks/insights/spectrum-bands-5g-world/….

ACuriousMind

how exactly the carrier wave frequency affects your bandwidth depends on how exactly your technology works - there is only a very general rule that higher frequencies give you more bandwidth with most technologies

ACuriousMind

4:08 PM

ugh, it's too warm

Mad

4:25 PM

It is

i was in my department doing work ( i work there as a repairman )
i died! its so hot, pulling all these cables from old laboratories and moving old oil pumps. it killed me

37 degrees or something! (Celsius)

ACuriousMind

for a ghost you're still communicating pretty well :P

Mad

Hehe

You would not believe how old this stuff in the laboratory is, somehow, the department decided to lock some rooms for 30 years and not use them. and we are "allowed" now to clean them out...

Theres equipment there, that at the time, probably cost a fortune!

Now belongs to the garbage...

ACuriousMind

oh, I'll believe that alright

I've seen corners of university labs where no one's been around for decades

Mad

4:41 PM

Sadly, the archieving is done so bad, we had no idea what is what and what are inside the boxes or inside the chemical glas containers, it was not fun to be honest, everytime i go there to do work, i am a bit scared, one time one of the pumps had vacuum inside, and when i opened it, a huge gus of streaming came right by my face, i was pretty sure i am a dead man, god only knows what the hell they had inside, it turned out to be air.

ACuriousMind

sacrificing students to suboptimal safety procedures is also a time-honored tradition :P

Mad

haha

we had a little panic today, in one of the boxes, there was a sign of radioactivity, the box contianer did not seem to contain any radio active things, we all stepped instantly out, who the hell wanna play with that? we got a geigermeter, felt like that tv show chernobyl, was a false alarm, someone played a bad joke :d

ACuriousMind

there was an apocryphal story when I was a student that they found a bunch of radioactive materials just sitting in an old cabinet in a lab that had been used as an office for decades

I don't know whether it's true, but it wouldn't have surprised me much

Mad

Thats no fun!! the people inside would have devoleoped some serious issues!

ACuriousMind

indeed, if it's true it's not very funny!

Mad

4:46 PM

Honestly what the hell, i ask myself, why dont people sort their equipment well? they just threw stuff and locked it, like its nothing. if they actually sorted stuff right, it would not have been such a hassle to clear out the labs.

ACuriousMind

I'd guess the research group that was in these labs disintegrated for some reason and no one was in charge of cleaning up after them

Mad

Actually, thats actually what happened, the stuff we cleaned belongs to groups that no longer exists, nevertheless, i wonder why when they disintegrated did not get rid of their equipment? they were the ones who actually knew whats inside. now we got to tippy toe around the machinery

ACuriousMind

I mean, yes, in a perfect world responsible people would do that and clean up

but in practice, if they know they're not staying they don't really have any incentive to do that :P

Mad

Departments should enforce that!

ACuriousMind

it's very difficult to force people to do anything if they know they're not staying!

Feynman_00

4:57 PM

@Mad Didactic labs don't have dangerous radioactive material

Mad

What is didactic labs?

Feynman_00

Labs for students

ACuriousMind

I'm not sure what labs for students are :P

Mad

I think he means the labs, where students do expirments, but i am not assigned to clean those.

Feynman_00

I should stop quoting without reading the whole conversation

That's a bad habit of mine

ACuriousMind

5:08 PM

also I vividly remember at least one lab course I did where we definitely handled radioactive materials you wouldn't want to have swallowed :P

Feynman_00

Well, you wouldn't want to swallow even non radioactive ones :P

I just used some Polonium and Uranium last year

ACuriousMind

the most hazardous thing I ever encountered in a lab was a stroboscope, though (I was very hungover that day and staring at a colorful spinning top under stroboscope light was, uh, not beneficial)

Feynman_00

Just kidding, I remember only Caesium

@ACuriousMind Does Pauli Effect apply to you?

ACuriousMind

no, I generally was pretty good at doing labs

the only thing that ever really malfunctioned/broke was a desk chair that collapsed when I sat on it :P

Mad

i hate labs, i was never good at them , i hated every minute i was forced to do an experiment. and i still do whenever i must. The most pain experianced by any man on this planet is stairing at the colours of light on atoms or optics in a dark room.

Feynman_00

5:22 PM

@ACuriousMind Tu quoque, Brute fili mi!

ACuriousMind

I mean, I didn't particularly enjoy a lot of them, but that's neither here nor there

Feynman_00

@ACuriousMind What about Field Theory classes?

ACuriousMind

I didn't have any dedicated classical field theory classes, and I loved QFT and CFT

Feynman_00

What is CFT? QCD?

ACuriousMind

conformal field theory

Feynman_00

5:33 PM

I didn't know that was a thing :(

ACuriousMind

now you do!

no need to be sad about it :P

Feynman_00

I think/hope I'll have that somewhere in my grad courses

I did a good job managing my time so I have two spare months. It's finally time to teach myself differential geometry

DIRAC1930

7:16 PM

Is whether an isolated system in a non-equilibrium state thermalizes dictated by the form of the interaction between particles?

If I take a simple $1D$ model with $N$ electrons interacting through the exchange interaction between neighbouring lattice sites, would I be able to show numerically that $\hat{U}^\dagger\hat{\rho}(0)\hat{U} = \hat{\rho}_{eq}$?

@ACuriousMind What's the simplest isolated quantum system that's known to thermalize?

ACuriousMind

@DIRAC1930 Since we usually look at thermodynamic systems in the limit $N\to\infty$, I'm not sure that's a well-defined question :P

thermal equilibrium is a convenient fiction

in general, our belief in thermalization is just the H-theorem

the whole point of statistical mechanics is that we don't know enough to actually do normal physics and just do time evolution on the system

if you know enough about a system to start with some $\rho$ and just evolve that through time, why the heck would you try to do statistical mechanics on it?

user4539917

7:32 PM

Those who try end up suicidal.

ACuriousMind

@user4539917 what?

user4539917

That's a famous quote from a stat mech textbook

re: Boltzmann et al

ACuriousMind

No, the quote is just that several people who did stat. mech. commited suicide

not that they tried to do stat. mech. on a system where it wasn't needed

Feynman_00

And this is how I decided to part ways with Stat mech

DIRAC1930

Say if I had a 10 particle isolated system in a state $|\psi>$ with $<E>$ fixed. Would I eventually find the distribution of states to be $p_i=e^{-\beta E_i}$ where $E_i$ are the energy levels of the states?

It just seems weird that from stat mech, we just assume that if we don't know anything about an isolated system, that it is in equilibrium. Say if I don't know anything about the universe (and assume it's isolated), if I just assume it's in equilibrium then I would be completely wrong.

How can how much I know about a system dictate whether a system is in thermal equilibrium or not.

Feynman_00

7:40 PM

Jokes aside, I just happened to like fundamental interactions more

ACuriousMind

@DIRAC1930 10 particles is very far from $N\to \infty$

user4539917

Sorry, joke removed.

ACuriousMind

I don't think anyone claims that a system of 10 particles is usefully modelled by the usual assumptions of equilibrium stat. mech.

equilibrium stat. mech. is not a fundamental theory in the sense that it claims to be applicable to all situations

it's "laws" are not laws you can just apply to a 2 particle system or whatever

an isolated system isn't going to magically thermalize, that's not the point - the point of eq. stat. mech. is that you consider situations where the interaction with the environment will lead to one of the ensembles being applicable

sometimes you have situations where you know the energy of a system but not much else - that's the MCE

DIRAC1930

But why should what I know dictate what the system is actually doing?

ACuriousMind

@DIRAC1930 it doesn't!

the probability density/density matrix in stat.mech. is a description of your knowledge of the system, not anything real

(there are interpretations of QM where this is true of all quantum states, but let's not derail)

if you try to do eq. stat. mech. on a system that's very far from equilibrium, you just won't get very good results

but experience tells us that a lot of systems are usefully modeled by the equilibrium assumption

DIRAC1930

7:48 PM

Is the equilibrium assumption this equal probabilites of microstates for an isolated system thing?

ACuriousMind

the "equal probabilities" is specific to the MCE

we've been over this before

DIRAC1930

Yes, thats the only one I'm focussing on for the moment

Feynman_00

Is Boltzmann distribution the same regardless the ensemble you use?

ACuriousMind

@Feynman_00 not sure what you mean: the Boltzmann distribution is by definition just the probability distribution of the equilbrium state in the CE

DIRAC1930

Let me see if I understand this correctly. If i stumble on a random isolated system and I know the mean energy to be $E$, the most probable distribution of states will be given by $\hat{\rho}=e^{-\beta H}$

ACuriousMind

7:52 PM

no

what does "random" in "random isolated system" even mean?

Feynman_00

@ACuriousMind Ok, this is what I knew but then I read on wiki you can derive it in MCE, CE and GCE

ACuriousMind

@Feynman_00 I don't know what that means: The equilbrium state in MCE is just uniform over all states with the same energy

(I think I've now produced all possible misspellings of "equilibrium" over the last few days :P)

DIRAC1930

The equilibrium distribution in MCE is $\hat{\rho}=e^{-\beta \hat{H}}$

Feynman_00

@DIRAC1930 That is CE

ACuriousMind

^that

MCE is just uniform over all states with a specific energy

Feynman_00

8:00 PM

Information theory approach is so different from standard approach (that I don't know)

In the information theory approach one makes Shannon entropy stationary and the distribution is of the form $\rho=Z^{-1}\exp(-\sum_i \lambda_i R_i)$ (where $R_i$ are the observables) even in non equilibrium situations. The information is encoded in the average values of the observables. If they are all constant, we have equilibrium

In the CE the only known observable is the Hamiltonian

@ACuriousMind en.m.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics here in the section "Derivations"

DIRAC1930

@Feynman_00 That's the derivation I saw from Susskind's lectures

Feynman_00

@DIRAC1930 Which one? The information theory approach or the one in the link?

DIRAC1930

8:22 PM

The way in the link

More Anonymous

8:53 PM

Another way of deriving the Maxwell distribution is to make use of isotropy, relative velocity and the fact these are distinguishable particles.

DIRAC1930

9:06 PM

If I have $N$ connected boxes (with a total constrained mean energy $<E>$) with different mean energies $E_i$, the occupation number $n_i$ is given by $n_i=e^{-\beta E_i}$

I think Landau does a similar thing in his book

But the density matrix will be $\hat{\rho}=\frac{1}{N}$ or something I think

I think his construction is the MCE

But I don't know how those $n_i$'s are useful in QM then

Unless $n_i$ counts the number of degenerate energy eigenstates

DIRAC1930

9:44 PM

Anyone?

DIRAC1930

10:12 PM

Susskind was calculating the Boltzmann distribution and not the MCE

fqq

11:42 PM

@DIRAC1930 no, as we told you several times over the last few days that's just not true for unitary evolution

in particular the system you described (for finite $N$) has a finite-dimensional Hilbert, so strictly speaking it's periodic, $\rho(k \tau_P) = \rho(\tau_P)$ for some finite time $\tau_P$ and all $k\in \mathbb{N}$. Thermalisation is a bit more subtle, but if you are studying quantum statmech now IMO you should not worry about that

ACuriousMind

you don't even need to go quantum for that, there's also classical Poincaré recurrence

stat. mech. is a very successful scam :P

fqq

it's something along the line that expected values of local operators become the same as they would be in the equilibrium state, $\lim_{t\to\infty} tr (\rho(t)\mathcal{O}) = tr(\rho_{eq}\mathcal{O})$ with extra subtleties on the order of large $N$/long $t$ limits

@ACuriousMind exactly it's not a quantum thing!

ACuriousMind

I'm sure this is partly due to the pretty terrible course I took on it, but I've never worried about stat. mech. much. It works sometimes, and all you need to pass it is compute some polylogarithmic integrals :P

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