Bohmian Mechanics Revisited

Yang Song, Yujun Yang, Fu-Ming Guo +1 more

Abstract The ionization process of a hydrogen-like atom in the intense laser field is studied by the Bohmian-mechanics method. We propose a criterion for atomic ionization based on the total energy of a Bohmian particle (BP): when it is larger than or equal to zero, ionization occurs, when it is lower than zero, no ionization occurs. We find that the time-dependent ionization probabilities calculated by the Bohmian-mechanics and projection methods are almost the same under different laser parameters. Two typical Bohmian trajectories are selected to analyze the ionization process. The consistency between the time-dependent ionization probabilities calculated by the two methods is quantitatively analyzed from the aspect of the probability density of the wave-function.

Arthur I. Fine

Claudia Zander, Angel Ricardo Plastino

We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space. The other partial measure corresponds to the correlations associated with the phase of the joint wave function, and describes the non-separability of the Bohmian velocity field. The sum of these two components is equal to the total entanglement of the joint quantum state, as measured by the linear entropy of the single-particle reduced density matrix.

Weixiang Ye

We systematically analyze Holland's local expectation values within Bohmian mechanics, referring to them as weak actual values to emphasize their connection with weak measurement theory. We derive the exact time evolution equation for these quantities along a Bohmian trajectory and formally establish their correspondence with the real part of the weak value under position postselection. The explanatory power of this framework is demonstrated by revisiting a recent waveguide experiment: we show that the measured quantity corresponds to the imaginary part of the momentum weak value, which reflects the spatial decay of the wave field, not the particle velocity. This cleanly clarifies the distinct physical roles of the real and imaginary parts of weak values.

Antonio Boulhosa Nassar, Salvador Miret-Artés

K. Berndl, M. Daumer, D. Dürr +2 more