Recent content by Tianwu Zang

Yes I think you get the point. It seems that Ito calculus uses a different method for changing the variables. I am really unfamiliar with this area before so your link really helps. Thanks a lot!

Dear all, I have a question about the variable substitution in Langevin equation and Fokker-Planck equation and this has bothered me a lot. The general Langevin equation is: $$\frac{dx}{dt}=u(x)+\sqrt{2 D(x)}\eta(t)$$ and the corresponding Fokker-Planck equation is thus: $$\frac{\partial...

Hi all, What is the potential generated by a electric loop? I have found two ways to sovle the problem. One is since the charge density does not change with time, we can write it as \phi(\vec{r_{0}})=\oint\frac{\rho_{static}}{|\vec{r}-\vec{r_{0}}|}d\vec{l}. But what is \rho in this loop? Is...

Hmm, I see. Your word "distribution of energy on the different modes is precisely the result of reaching equilibrium with a minimum free energy" made me clear. Thanks a lot.

Homework Statement In a reservoir there are three balls. There is a spring(the weight of spring is negligible) with elastic coefficient k between each two balls(small enough, like two particles). Suppose the center of gravity of the system does not move, and the mass of each ball is m. Suppose...

It is well known that for an isolated system, the normal mode frequency of a N-body harmonic oscillator satisfies Det(T-\omega^{2}V)=0. How about a non-isolated, fixed temperature system? In solid state physics I have learned that in crystal the frequency does not change, but the amplitude of...

So solving the eigenvalue of matrix in infinite dimension is not the same with the process to solve the eigenvalue of matrix in finite dimension? I know the determinant of a-\alphaI is \alpha^{n} when the matrix is finite. How about the determinant when it is infinite? I am not very familiar...

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Hi all, the annihilation operator satisfies the equation \hat{a}|n>=\sqrt{n}|n-1> and \hat{a}|0>=0 so the matrix of \hat{a} should be http://www.tuchuan.com/a/2010020418032158925.jpg and zero is the only eigenvalue of this matrix. The coherent state is defined by...

we know that vector potential in a resonator satisfies the equation \intA(\lambda)A^{*}(\lambda^{'})dV=4\pic^{2}\delta_{\lambda\lambda^{'} So how about in cavity of arbitrary shape? Does this equation still valid? Thanks!