Related papers: On the Classical Description of Nuclear Motion

In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a sort of geometrical dequantization…

A general method of quantum-to-classical reduction of quantum dynamics is described. The key aspect of our method is the similarity transformation of the Liouvillian, which provides a new perspective. In conventional studies of quantum…

Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…

We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…

The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…

Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…

In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…

Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…

We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…

In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf…

We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…

In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…

We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…

Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schr\"odinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without…