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We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman propagator of a particle quantum mechanically moving under a time independent potential., Comment: arXiv admin note: substantial text overlap with arXiv:1909.05123

We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman path integral expression for the Feynman propagator of aparticle quantum mechanically moving under an external electromagnetic time independent potential

We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this formalism the quantum evolution is described through a dynamical system of infinite dimension for the position, the momentum and all dispersions. Usually the system is truncated to have a finite dimensional one, however, in this case equations of motion decouple and the system can be solved. For a specific set of initial conditions we find that the time dependent dispersion in position is always around the classical trajectory., Comment: 1 figure

The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential operator. When a verified method is relativistic, the relativistic exponential operator should be expanded in the semirelativistic power series. The use of the obtained exponential operator for a derivation of the Foldy-Wouthuysen Hamiltonian makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation, while this possibility may need a greater computational effort., Comment: 14 pages, final version

Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The origin of these difficulties is discussed, and it is shown how they can be avoided by means of another approach, based on different solutions of the same equation. Results for the same potentials, obtained by this latter method are presented and a comparison is made., Comment: 4 figures

We propose a scheme for generating remote continuous steady-state entanglement of output light leaked from optomechanical system, in which two mechanical oscillators are coupled through long-range Coulomb interaction. we show that the entanglement of output light is affected by the detuning and the strength of the Coulomb interaction. We also demonstrate that two movable mirrors and two light beams can be entangled in the steady state. We suggest an experimental readout scheme to fully verify the characteristic of entangled state., Comment: 5 pages,2 figures

Here, we compare the behavior of the quantum discord, 1-norm geometric quantum discord and concurrence under the effect of decoherence for XXX Heisenberg spin chain. Their dependencies on temperature and coupling constant are presented in detail. By a comparison between them we can see that quantum discord and 1-norm geometric quantum discord are more robust than the concurrence against decoherence in the sense that quantum discord and 1-norm geometric quantum discord takes a nonzero value and decrease asymptotically, while the concurrence is zero in a large range of parameters including temperature and coupling constant. Moreover, we find that there is no simple relative ordering between 1-norm geometric quantum discord and quantum discord. This result contradicts the information which provided in some papers., Comment: 13 pages, 8 figures

The recently published "Oxford Questions" are supplemented with annotations concerning: doctrine of wave packets collapse (and sub- sidiarily Schrodinger's cat thought experiment), description of quan- tum measurements respectively interpretation of uncertainty relations., Comment: 7 pages

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed., Comment: Major update. Improved main statements. 21 pages

We show (an earlier conjecture of the last two authors) that the momentum and position operators of mu-deformed quantum mechanics for -1/2 < mu < 0 are not Accardi complementary. We also prove some related formulas that were conjectured by the same authors., Comment: 13 pages

In this note we show that the momentum and position operators of $\mu$-deformed quantum mechanics for $\mu > 0$ are not Accardi complementary in a sense that we will define. We conjecture that this is also true if $-1/2 < \mu < 0$., Comment: 9 pages

In the case of simple graded manifolds utilized in supermechanics, supervector fields and exterior superforms are represented by global sections of smooth vector bundles., Comment: 6 pages, LaTeX