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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., 1 figure

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., 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., 13 pages, 8 figures

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., 6 pages, LaTeX