This Research Topic is Volume II of a series. The previous volume can be found here:

Quantum and Semiclassical Trajectories: Development and ApplicationsTrajectory-based approaches to quantum dynamics have been developed and applied to describe a range of quantum processes, including nonadiabatic dynamics, quantum tunneling, quantum entanglement, geometric phase effects, and others. Such quantum trajectory methodologies have computational advantages for the numerical simulation of large quantum problems, particularly in many-dimensional systems, where “on the fly" electronic structure methods are often employed to calculate forces and couplings at the instantaneous trajectory coordinates. Thinking and computing with individual quantum trajectories and their ensembles provide both an intuitively-appealing conceptual perspective and a practical computational framework simulating and understanding important quantum effects in physical and chemical systems.

In this Research Topic, we hope to provide a broad overview of current work in trajectory-based approaches to quantum dynamics. The Topic aims to span the field, from the fundamental interpretational aspect of trajectory-based formalisms as an alternative way of understanding quantum physics and its classical limit and gaining physical intuition and visualization of the dynamical evolution of physical systems to meeting practical challenges of many-dimensional quantum dynamics by exploiting the computational efficiency of classical trajectory methods generalized to the quantum realm.

We welcome researchers to contribute Original Research and Review papers for this Research Topic sharing the most recent ideas in the field of the trajectory descriptions of quantum mechanics. Potential topics include, but are not limited to：

• Quantum & Semiclassical trajectories methods

• Bohmian mechanics

• Wave-free quantum mechanics/many interacting worlds

• Lagrangian-based numerical methods (e.g., Dirac-Frenkel)

• Atomic and molecular physics

• Chemical dynamics

• High-resolution spectroscopy

• Noether’s theorem, symmetry, and conservation laws

• Quantum foundations

• Relativistic effects in electronic structure and dynamics

This Research Topic is Volume II of a series. The previous volume can be found here:

Quantum and Semiclassical Trajectories: Development and ApplicationsTrajectory-based approaches to quantum dynamics have been developed and applied to describe a range of quantum processes, including nonadiabatic dynamics, quantum tunneling, quantum entanglement, geometric phase effects, and others. Such quantum trajectory methodologies have computational advantages for the numerical simulation of large quantum problems, particularly in many-dimensional systems, where “on the fly" electronic structure methods are often employed to calculate forces and couplings at the instantaneous trajectory coordinates. Thinking and computing with individual quantum trajectories and their ensembles provide both an intuitively-appealing conceptual perspective and a practical computational framework simulating and understanding important quantum effects in physical and chemical systems.

In this Research Topic, we hope to provide a broad overview of current work in trajectory-based approaches to quantum dynamics. The Topic aims to span the field, from the fundamental interpretational aspect of trajectory-based formalisms as an alternative way of understanding quantum physics and its classical limit and gaining physical intuition and visualization of the dynamical evolution of physical systems to meeting practical challenges of many-dimensional quantum dynamics by exploiting the computational efficiency of classical trajectory methods generalized to the quantum realm.

We welcome researchers to contribute Original Research and Review papers for this Research Topic sharing the most recent ideas in the field of the trajectory descriptions of quantum mechanics. Potential topics include, but are not limited to：

• Quantum & Semiclassical trajectories methods

• Bohmian mechanics

• Wave-free quantum mechanics/many interacting worlds

• Lagrangian-based numerical methods (e.g., Dirac-Frenkel)

• Atomic and molecular physics

• Chemical dynamics

• High-resolution spectroscopy

• Noether’s theorem, symmetry, and conservation laws

• Quantum foundations

• Relativistic effects in electronic structure and dynamics