Recent content by Quantioner

Because $$ \Delta(p) = \frac{1}{p^2-m^2+i\epsilon} = -i \int_0^\infty d\alpha ~e^{i(p^2 - m^2 +i\epsilon)\alpha} $$ Thus $$ \Delta(x) = \int \frac{d^4 p}{(2\pi)^4} e^{-ipx} \Delta(p) \\ = -i \int_0^\infty d\alpha \int \frac{d^4 p}{(2\pi)^4} ~e^{-ipx+i(p^2 - m^2 +i\epsilon)\alpha} \\ = -i...

I'm sorry that the definition should be changed to Ventropy[op_] := -Tr[op.MatrixLog[op]] op = ({ {1/2, 1/3}, {1/3, 1/2} }); Ventropy[op] the result is $$ -\frac{2}{3} \left(\frac{\log (6)}{2}-\frac{1}{2} \log \left(\frac{6}{5}\right)\right)+\frac{\log (6)}{2}+\frac{1}{2} \log...

Hi, valesdn. http://en.wikipedia.org/wiki/Von_Neumann_entropy gives the definition of Von Neumann entropy. op is just an example, you can change it to whatever operator you like.

You should re-define the entropy function since the original one can not be applied in quantum case. BTW, the von Neumann entropy of a density operator ##\rho## is ##{\rm Tr}[\rho \ln(\rho)]## but not ##{\rm Tr}[\rho \log_2(\rho)]##. Ventropy[op_] := -Tr[op MatrixLog[op]] op = ({ {1/2, 1/3}...

The Feynman propagator is $$ G_{F}(x) = \int d^4p \, \frac{e^{-ip x}}{p^2 - m^2 + i\epsilon}. $$ I want to understand why the directions of Wick rotation in position space and momentum space are contrary. Every book I find says something like "we should keep ##xp## unchanged", but why? As we...

You're always welcome.

I will reply you tomorrow.

Luckily, I have defined such a function. ptrace[mat_, d_, k_] := With[{d1 = Length[mat]/d}, Table[Total[ mat[[FromDigits[({Reverse, Identity}[[k]])[{m, #}], d] - d, FromDigits[({Reverse, Identity}[[k]])[{n, #}], d] - d]] & /@ Range[d]], {m, 1, d1}, {n, 1, d1}]] (*partial...

Hi, I use Mathematica to define a function sg[x,k] to calculate the Svein-Graham sum and plot some figures for ##x \in [1,2]## with ##k## varies from 1 to 5. sg[x_, k_] := Module[{f}, f[y_] := #^y &; (FoldList[f[x], x, Range[k - 1]] // Total) + 1] Plot[sg[x, #], {x, 1, 2}] & /@ Range[1, 5]

I am use Mathematica for a while. One can define his own functions to calculate all these quantities, Atlas 2 is not free.

The code is as follow: psi = {1, 1, Cos[\[Psi]/2] - Sin[\[Psi]/2], Cos[\[Psi]/2] + Sin[\[Psi]/2]}/2; con = 2 Abs[psi[[1]] psi[[4]] - psi[[2]] psi[[3]]] // FullSimplify

Thanks! I have read it. It's a very interesting first class to me.

Hello, there. I use the name "Quantioner" in PF, which means that "I am learning quantum information". I study Mathematics when I was an undergraduate, and now change to Physics because I think it's more meaningful. Since I am a newer to Physics, please forgive me for asking some questions which...