Stabilization of quantum energy flows within the approximate quantum trajectory approach

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• The de Broglie-Bohm formulation offers an alternative to the Schrödinger equation using quantum trajectories.
• While trajectory dynamics scale favorably with system size, they are unstable due to quantum potential singularities.
• Approximate quantum potentials are stable but can yield inaccurate forces in bound systems.

Purpose of the Study:

• To improve the numerical stability and accuracy of the de Broglie-Bohm formulation.
• To address inaccuracies in approximate quantum potentials for bound systems.
• To enhance the description of zero-point energy in quantum dynamics.

Main Methods:

• Developing an approximate quantum potential by fitting the nonclassical momentum operator.
• Introducing a semiempirical friction-like force to compensate for errors in the approximate quantum potential.
• Applying the method to one-dimensional models relevant to nuclear dynamics.

Main Results:

• The proposed friction-like force significantly improves the description of zero-point energy in bound systems.
• The modified formulation demonstrates enhanced numerical stability and accuracy.
• The method shows promise for simulating nuclear dynamics.

Conclusions:

• The semiempirical friction-like force is an effective correction for approximate quantum potentials in the de Broglie-Bohm formulation.
• This approach enhances the quantitative accuracy of quantum trajectory simulations.
• The findings are particularly relevant for studies in nuclear dynamics and quantum chemistry.