Numerical study of multiparticle production in $\phi^4$ theory: comparison with analytical results

We develop a numerical method to compute the probabilities of multiparticle production in weakly coupled scalar theories. Our technique is based on D.T. Son’s semiclassical method of singular solutions. Applying it to the process $1 \to n$ in the unbroken four-dimensional $\lambda {{\phi }^{4}}$ theory, we reproduce the known results at $1 \ll n \ll {{\lambda }^{{ - 1}}}$.