Tunneling problems by quantum Monte Carlo

We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the single-particle (tunneling in the double-well potential) and many-body systems (e.g., vacuum-to-vacuum transitions), and gives directly the instanton shape and tunneling amplitude. Most importantly, transition amplitudes may be calculated to arbitrary accuracy (being limited solely by statistical errors) no matter how small are their absolute values.