Abstract
Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational tool to simulate quantum systems consisting of many particles, a very demanding computational task. In this paper, we present a novel ab-initio approach to solve the many-body problem for bosonic systems by evolving a system of one-particle wavefunctions representing pilot waves that guide the Bohmian trajectories of the quantum particles. In this approach, quantum entanglement effects arise due to the interactions between different configurations of Bohmian particles evolving simultaneously. The method is used to study the breathing dynamics and ground state properties in a system of interacting bosons.
Highlights
Numerical simulation of the quantum dynamics of many-body systems is plagued by the dimension of the Hilbert space which increases exponentially with the number of particles
While this interpretation does not alleviate the need for dealing with many-dimensional functions, the prospect of replacing the full many-particle wavefunction by single-particle wavefunctions that guide the Bohmian particles in the physical space was recently explored[19]
The pilot waves are the full wavefunction projected they are called on the coordinates of all the particles conditional wavefunctions (CWs)[27]
Summary
Numerical simulation of the quantum dynamics of many-body systems is plagued by the dimension of the Hilbert space which increases exponentially with the number of particles. We see from this equation that the pilot waves corresponding to different particles interact indirectly through the last three terms of Eq (3).
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