Time-dependent quantum Monte Carlo and the stochastic quantization
arXiv:0706.3579 · doi:10.1063/1.2779038
Abstract
We examine the relation between the recently proposed time-dependent quantum Monte Carlo (TDQMC) method and the principles of stochastic quantization. In both TDQMC and stochastic quantization particle motion obeys stochastic guidance equations to preserve quantum equilibrium. In this way the probability density of the Monte Carlo particles corresponds to the modulus square of the many-body wave function at all times. However, in TDQMC the motion of particles and guide waves occurs in physical space unlike in stochastic quantization where it occurs in configuration space. Hence the practical calculation of time evolution of many-body fully correlated quantum systems becomes feasible within the TDQMC methodology. We illustrate the TDQMC technique by calculating the symmetric and antisymmetric ground state of a model one-dimensional Helium atom, and the time evolution of the dipole moment when the atom is irradiated by a strong ultrashort laser pulse.
40 pages, 4 figures, replaced fig.4
References in corpus (10)
- Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
- Reconciling Semiclassical and Bohmian Mechanics: I. Stationary states
- Quantum tunneling dynamics using hydrodynamic trajectories
- Modified de Broglie-Bohm approach to quantum mechanics
- Time-dependent quantum Monte Carlo: preparation of the ground state
- A generalization of the Fenyes-Nelson stochastic model of quantum mechanics
- Quantum initial value representations using approximate Bohmian trajectories
- Correlated non-perturbative electron dynamics with quantum trajectories
- A new challenge for time-dependent density-functional theory
- Quantum trajectory perspective of atom-field interaction in attosecond time scale