Related papers: A Generalized Analytical Mechanics in which Quantu…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential…
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…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple…
It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive…
Computational chemistry at the atomic level has largely branched into two major fields, one based on quantum mechanics and the other on molecular mechanics using classical force fields. Because of high computational costs, quantum…
Conceptual analogies among statistical mechanics and classical (or quantum) mechanics often appeared in the literature. For classical two-body mean field models, an analogy develops into a proper identification between the free energy of…
We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where 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…
Quantum and classical mechanics share a common algebraic formalism which is expressed naturally in the language of category theory. A third realization of this formalism is the so-called hyperbolic quantum mechanics where split-complex…