New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

Shinil Cho

Salah Badawi Doma, N. A. El-Nohy, Mahmoud Ahmed Salem

Balázs Hetényi, Eran Rabani, B. J. Berne

We propose a new method to calculate ground state position dependent observables in quantum many-body systems. The method, which we call the path-integral diffusion Monte Carlo (PI-DMC) method, is essentially a combination of path-integral Monte Carlo (PIMC) and diffusion Monte Carlo (DMC) methods. The distribution resulting from a DMC simulation is further propagated in imaginary time by PIMC sampling. Tests of the new method for simple cases such as the harmonic oscillator, a double well, and a set of ten coupled harmonic oscillators show that the results for several observables converge rapidly to the exact result.

Ivan P. Christov

We study one-dimensional (1D) and 2D helium atoms using a new time-dependent quantum Monte Carlo (TDQMC) method. The TDQMC method employs random walkers, with a separate complex-valued guiding wave attached to each walker. The ground state is calculated by a self-consistent solution of complex-time Schrödinger equations for the guiding waves and of equations for the velocity fields of the walkers. Our results show that the many-body wavefunction and the ground state energy of the model atoms are very close to those predicted by the standard diffusion quantum Monte Carlo method. The obtained ground state can further be used to examine correlated time-dependent processes which include, for example, interaction of atoms and molecules with external electromagnetic fields.

Ivan P. Christov, Dan Dumitraş

Masuo Suzuki