Related papers: Quantum Potential and Symmetries in Extended Phase…
The action reaction principle is violated by the projection of state in some simple quantum measurements. A formulation of Quantum Mechanics in an extended phase space is proposed in order to restore the action reaction principle. All…
A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
In this paper we suggest a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
The motivation of this work is to get an additional insight into the irreversible energy dissipation on the quantum level. The presented examination procedure is based on the Feynman path integral method that is applied and widened towards…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We analyze the canonical quantum dynamics of the isotropic Universe in a metric approach by adopting a self-interacting scalar field as relational time. When the potential term is absent we are able to associate the the expanding and…
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time. It has been shown that canonical and path-integral approaches may yield different results,…
In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
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…
The existence of non-vanishing Bohm potentials, in the Madelung-Bohm version of the Schr\"odinger equation, allows for the construction of particular solutions for states of quantum particles interacting with non-trivial external potentials…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Semi-classical methods of statistical mechanics can incorporate essential quantum effects by using effective quantum potentials. An ideal Fermi gas interacting with an impurity is represented by a classical fluid with effective…
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic…