Phase space representation of quantum dynamics

Vladimir S. Filinov

Gabino Torres-Vega

Probability densities in phase space containing quantum dynamics information are very useful. However, is there a true phase space representation of Quantum Mechanics?

Kazuma Nagao

Xiangsong Cheng, Xin He, Jian Liu

Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys.145, 204105 (2016); 151, 024105 (2019); J. Phys. Chem. Lett.12, 2496 (2021), non-covariant phase space functions, time-dependent weight functions, and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system. The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrodinger equation. The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite. We also prove that the triangle window function approach, albeit proposed as a heuristic empirical model in J. Chem. Phys.145, 144108 (2016), is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.

Jincheng Zhang

This paper investigates the application of dynamic phase-space analysis to quantum field theory, aiming to enhance predictive power through a novel approach. Traditional approaches often treat the system's state as static, limiting the model's ability to capture complex evolution. We propose a system where the phase space itself dynamically updates based on the system's evolution, offering a more comprehensive and potentially more accurate representation of the underlying physics. This work introduces a method for continuously refining the phase space representation, incorporating the system's state changes directly into the analysis. The core mechanism centers around a modified time-stepping scheme that adapts to the system's dynamics, leading to improved predictive capabilities. This paper provides a foundational framework for dynamic phase-space modeling within the context of quantum field theory.

Hai-Woong Lee