ok, so can I say <e^{\phi(t)+\phi(t+\tau)}>=<e^{\phi(t)+\phi(t)+\phi(\tau)}> since W(t+\Delta t)=W(t)+W(\Delta t). Next we can say <e^{\phi(t)+\phi(t)+\phi(\tau)}>=<e^{2\phi(t)}><e^{\phi(\tau)}> because <\phi(t)\phi(\tau)>=0
Let \phi(t) be a Brownian Walk (Wiener Process), where \phi\in[0,2\pi). As such we work with the variable z(t)=e^{i\phi(t)}. I would like to calculate
E(z(t)z(t+\tau))
This is equal to E(e^{i\phi(t)+i\phi(t+\tau)}) and I know that
E(e^{i\phi(t)})=e^{-\frac{1}{2}\sigma^{2}(t)}, where the...
There seems to be a curious connection between Brownian Motion, stochastic diffusion process, and EM.
http://en.wikipedia.org/wiki/Stochastic_processes_and_boundary_value_problems
I was hoping to share and to have someone add some insight on on what it means that the Dirichlet boundary...
This can be very useful, so I thought i'd share.
If you edit the
> Wolfram Research\Mathematica\8.0\SystemFiles\FrontEnd\TextResources\Windows\MenuSetup.tr
file you can make Strl+Shift+C copy not plain but in LateX format. Very useful. Look for the line in the file that says "&LaTeX"...
this sounds like a question that should be answered somewhere, but i cant find it.
how many quantum numbers does it take to specify the state of a spin 1/2?
1. if it points along z, then just 1: the eigenvalue of Sz will do (up to global phase)
A. whether or not in a B field
B. if...
im not sure thats any better. just because 200 years ago we could not "point to" or manipulate say cooper pairs or atoms, doesn't mean they dont exist and don't have an effect.
this is a real problem in physics, how do we see and manipualte, people are discovering new ways every so often...
so i think it works for any function with a taylor expansion (~analytic), because conjugation carries through addition and multiplication and so through powers and thus exponents
1. (z1 +z2)* = z1*+z2*
2. (z1 z2)* = z1* z2*
3. (z1^n)* = z1*^n
4. \left(\frac{1}{\text{z1}}\right)^* =...
yes, you are saying that information is a human construct and does not exit beyond us, like the alphabet or the idea of the color green.
this is true, the concept of information is 'artifical' in the sense that as a concept it is not ontological (does not exist), but like all human concepts...
this is very good, that is what i was asking! Thank you,
so it works almost all the time. do you know when, in what cases i should be careful when using it?
ie anytime i dont use fractions and logs, and exponetnials and trig funcs?
see my post right above yours, i know that the complex conjugate is only equal to the complex # itself when the number is real,
i am asking how to get the complex conjugate
i agree, i think this is the essence of heisengber uncertainty and infromation.
for something to be ontological (that it can exist), it must have effect, and must be also epistomological (knowable), we must be able to know about it, to learn it is there.
we can only deal with things we...
this is all true, and is a summary of grifits derivation, but it it doesn't tell you that the raising and lowering operators take you between nearest orthogonal states. what is they raised and lowered by two quanta of energy,
how do you know what the smallest quanta of energy is?
this is basically the answer to my question, but i do need to unravel its meaning:
1. holomorphic - basically well behaved, has derivatives.
2. phi(z) is real for z in reals, this is a hard condition, because often the form of the expression is not such, but i have found that the trick...
Hi,
i do not understand why i can find the FT of sin in mathematica using the built in function but not by integrating, even thoiugh they should be the same:
Integrate[Exp[i(ω-ω0) t,{t, -∞, ∞}, Assumptions ->ω0 el Reals && ω el Reals]
but the statment
FourierTransform[Sin[ω0 x]...
your question is very fundamental and basic, check the wiki on wavefunction.
the wavefucntion is a function of the phase space -> like position
the interpertation is not agreed upon but you can think of it as probabily density of finding the particle (matter) at some position.
yes it obeys the...
Following Griffiths derivation on pg 44 of the eigen-states of SHO Hamiltonian, he says that we can now find all eigenvalues, but doesnt say how he knows that a and a dagger will indeed take you between nearest neighboring orthogonal states.
in other words, how do we know the ladder operators...
well there is some interaction b/w the photon and the phonons, like in ion trapping, where you get dressed states of the phonon ladder and the qubit (some transition in say Yb+ (Monroe research)) which atomic transition (qubit) the light field can interact with.
on the other hand this is...
ok! so if you have a linewidth on your state (eg a non-ground state) then you can also `transition` within the linewidth with some small probabily, which would be incoherent and inelastic. the reason this is called spontaneous Raman scattering is because it only occurs sometimes?
-usually? maybe you can be a bit more explicit about what you mean by coherence? i was imagining that the phase and polarization of the outgoing photon is the same as the ingoing one
- this makes sense to me if i believe the that for processes on short time scales the effective...
In solids it is the interaciton b/w the phonons and photons that give a lower effective speed. not absorption & re-emmision. (see ZapperZ's post: https://www.physicsforums.com/showthread.php?t=511177 [Broken])
but in amorphous glass there are [B]no[B] phonons. So why does light 'slow down'...
ok that makes a bit more sense Cthugha, thank you.
so there are 2 scattering processes for an atom in free space:
1. the linear abs/emit
2. quadratic a, a-dagger combinations for the light field that emit a photon of the same energy but in a random direction? (should be quasi-random right...
to be honest im very confused now, is there any way you can describe the process to someone unfamilar with virtual photons but in a physics phd program
ok that is more strictly true since it modifies the SHE. but it also sheds some light on measrument and decoherence treating them as wavfunciton leaking from system with small #dof to a system with large #dof again see the post by zpower
If you are [I]really[I] interested in the subject i just found a great review article on decoherence and interpretations:
Decoherence, the measurement problem, and interpretations of quantum mechanics
Rev. Mod. Phys. 76, 1267–1305 (2005)
http://rmp.aps.org/abstract/RMP/v76/i4/p1267_1
Great Question!! I've been puzzling over this myself.
I think we are talking about physical information, as in one spin can contain 1 bit of information. it is either up or down. (or is it two since it also has direction?). When we measure it, to know it is there, must we be recieving...