Path integrals in Quantum mechanics

Path integral Monte-Carlo method

To make MC simulation of quantum oscillator [1-3] the "Boltzmann" factor   exp(-S) for the path x(t) is used where
    S = int L(t,t') dt = ∑i=1,N (xi+1 - xi )2/a + a xi2,
L(x,x') = x' 2 - x2,   x' = dx/dt and a is the time step.
Every iteration we change random xrnew = xr + dx,   dx = b (Rand - 0.5) and calculate the difference
    dS = S new - S old = dx [2(xnew + xr - xr+1 - xr-1 )/a + (xnew + xr )a]
Then in accordance with the "Boltzmann" factor we accept or reject new configuration...
a=1, b=1, N=100 are used.

Java Virtual Matchine compiles "on-fly" simple applications, therefore e.g. the Mandelbrot set applet is only 25% slower than the corresponding C program (results may depend on chips and JVMs). The PIMC applet above makes every "Step" 106 MC iterations for T=0.65 sec on Athlon1500+ and IE6 (you can see your time in the Status bar).

[1] M.Creutz, B.A.Freedman "A statistical approach to quantum mechanics"
Annals of Physics 1981, 132, 427
[2] Richard MacKenzie "Path Integral Methods and Applications" arXiv:quant-ph/0004090
[3] Tilman Sauer "The Feynman Path Goes Monte Carlo" arXiv:physics/0107010

updated 1 July 2004