Towards a mathematical theory of the Madelung equations: Takabayasi's quantization condition, quantum quasi-irrotationality, weak formulations, and the Wallstrom …
Even though the Madelung equations are central to many'classical'approaches to the
foundations of quantum mechanics such as Bohmian and stochastic mechanics, no …
foundations of quantum mechanics such as Bohmian and stochastic mechanics, no …
Governing without a fundamental direction of time: Minimal primitivism about laws of nature
EK Chen, S Goldstein - Rethinking the Concept of Law of Nature: Natural …, 2022 - Springer
Abstract The Great Divide in metaphysical debates about laws of nature is between
Humeans, who think that laws merely describe the distribution of matter, and non-Humeans …
Humeans, who think that laws merely describe the distribution of matter, and non-Humeans …
The unexpected resurgence of Weyl geometry in late 20th-century physics
E Scholz - Beyond Einstein: Perspectives on geometry, gravitation …, 2018 - Springer
Weyl's original scale geometry of 1918 (“purely infinitesimal geometry”) was withdrawn by its
author from physical theorizing in the early 1920s. It made a surprising comeback, however …
author from physical theorizing in the early 1920s. It made a surprising comeback, however …
Koopman analysis of quantum systems
Koopman operator theory has been successfully applied to problems from various research
areas such as fluid dynamics, molecular dynamics, climate science, engineering, and …
areas such as fluid dynamics, molecular dynamics, climate science, engineering, and …
Entropy-a guide for the perplexed
Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines
ranging from logic and statistics to biology and economics. However, a closer look reveals a …
ranging from logic and statistics to biology and economics. However, a closer look reveals a …
Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics
V Yordanov - Scientific Reports, 2024 - nature.com
In this paper, we present a stochastic approach to relativistic quantum mechanics. We
formulate the three fundamental principles of this theory and derive the Dirac equations …
formulate the three fundamental principles of this theory and derive the Dirac equations …
A discrete Schrödinger equation via optimal transport on graphs
Abstract In 1966, Edward Nelson presented an interesting derivation of the Schrödinger
equation using Brownian motion. Recently, this derivation is linked to the theory of optimal …
equation using Brownian motion. Recently, this derivation is linked to the theory of optimal …
Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie
A Khrennikov - Entropy, 2023 - mdpi.com
We start with a methodological analysis of the notion of scientific theory and its interrelation
with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and …
with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and …
Stochastic emergent quantum gravity
J Erlich - Classical and Quantum Gravity, 2018 - iopscience.iop.org
We present a stochastic framework for emergent quantum gravity coupled to matter. The
Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a …
Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a …
Bouncing oil droplets, de Broglie's quantum thermostat, and convergence to equilibrium
Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted
much attention because they are thought to offer a gateway to a better understanding of …
much attention because they are thought to offer a gateway to a better understanding of …