Stochastic Simulation of Quantum Systems and Critical Dynamics

We propose the transformation of the Langevin equation into an eigenvalue problem as the framework of the stochastic simulation of quantum systems. The potential of the method is illustrated by numerical results for the low-lying energy eigenvalues of one-particle systems. In the case of many degrees of freedom, the critical dynamics of a classical $d$-dimensional system is mapped onto the statics of an associated quantum system and of its classical ($d+1\mathrm{}$)-dimensional counterpart. These mappings yield an equality relating the dynamical critical exponent $\Delta$ and the static susceptibility exponents of three models.