I am trying to clarify the relation between random walk and diffusion, and the source book proposes the following which I can't get. Starting from the diffusion equation $$ \\frac{\\partial …

That tells us that we have to separate the Schrödinger equation into two, one equating the real parts of the two sides, and one equating the imaginary parts. The meaning of this imaginary …

Jan 7, 2021 · With this definition, the diffusion equation is time-reversal symmetric if, for all solutions $\rho (x,t)$, we have that $\rho (x,-t)$ is also a solution. Since this is clearly false, the …

Convection is the collective motion of particles in a fluid and actually encompasses both diffusion and advection. Advection is the motion of particles along the bulk flow Diffusion is the net …

Dec 6, 2022 · Note that diffusion equation is a particular case of Fokker-Planck equation, which describes many stochastic processes under rather general conditions. Another way to think of …

I know that the diffusion equation is a more general version of the heat equation. But what is the exact difference informally?

Dec 9, 2021 · The reason is that your dynamics with a given step $\ell$ does not fix the diffusion constant in different dimensions to be the same. So your diffusion constant in the 2d case is …

Jan 22, 2025 · Approximate discrete random walk as diffusion To simplify the discussion, we'll approximate the discrete random walk as a diffusion process, which is a good approximation …

Jul 30, 2020 · I read, that for normal diffusion the root mean square displacement $\\sqrt{\\langle x^2(t)\\rangle}$ (for particles at the origin) can be interpreted as the mean distance the …

This causes the equation's solutions to osculate instead of decay with time because $$ \exp (-Dt)=\exp (-iD't) $$ Which is why the Schrödinger equation has wave solutions like the wave …