Related papers: Deep Learning for Feynman's Path Integral in Stron…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and…
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new…
The quantum field theory in the presence of classical background electromagnetic fields is reviewed. We give a pedagogical introduction to the Feynman-Furry method of describing non-perturbative interactions with very strong electromagnetic…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
The emergence of classical behavior from quantum mechanics as Planck's constant $\hbar$ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined by the absorbing boundary. Trajectories that reach the absorbing wall are…
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information…
The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of…
We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider…
This paper theoretically analyzes the behavior of an atom driven by a strong electro-magnetic field. Moreover, besides traditional quantum mechanics method, we also investigate semiclassical approaches to this problem. We first performed…
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical…
Although Feynman integrals in general cannot be expressed as well-studied special functions, they can be calculated systematically and efficiently using the \texttt{AMFlow} method in combination with differential equations in the kinematic…