相关论文: On the mathematical treatment of the Born-Oppenhei…

In this comment we critically review an argument against the existence of objective physical outcomes, recently proposed by R. Healey [Foundations of Physics, 48(11), 1568-1589]. We show that his gedankenexperiment, based on a combination…

We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…

This paper gives a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies two famous approximation theorems; one is due to Auslander and Bridger and the other is due to Auslander and…

Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…

Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…

In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…

Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett., ${\bf 100}$, 123004 (2008)] is formulated for general Hohenberg-Kohn density functional theory and compared to the extended Lagrangian framework of first principles…

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…

We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…

The various recent studies on the applications of the Born-Oppenheimer approach in a closed gravity matter system is examined. It is pointed out that the Born-Oppenheimer approach in the absence of an a priori time is likely to yield…

While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of…

We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this…

Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…

Quantum simulation is widely regarded as one of the most promising routes to genuine quantum advantage, yet most existing approaches to quantum chemistry are formulated in terms of closed-system, unitary dynamics and ground-state…

Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the…

The present work provides a definitive answer to the problem of quantifying relaxation to equilibrium of the solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules. The beginning of the story dates back to a…

The Born-Oppenheimer approximation is widely used to investigate the properties of hydrogen-like systems and doubly heavy hadrons. However, the extent to which this approximation captures the features of such systems within potential models…

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the QED (quantum electrodynamics) sector…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…