Counterpropagating Wavepacket Solutions of the Time-Dependent Schroedinger Equation for a Decaying Potential Field

We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time coordinates, we obtain two distinct wavepacket solutions for the Schroedinger equation. The wavepackets counterpropagate in space at a constant velocity without any distortion or spreading thus retain their initial form at arbitrarily large distances.Comment: 10 pages, 4 figure

Symmetry Reduction of Lane-Emden Equation for Polytropes

We describe an ansatz for symmetry reduction of the Lane-Emden equation for an arbitrary polytropic index n, admitting only one symmetry generator. For the reduced first order differential equation it is found that standard reduction procedure do not admit any non-trivial Lie point symmetry. However some special solutions for the differential equation are obtained

Real-time emission spectrum of a hybrid atom-optomechanical cavity

We theoretically investigate the real-time emission spectrum of a two-level atom coupled to an optomechanical cavity (OMC). Using quantum trajectory approach we obtain the single-photon time-dependent spectrum in this hybrid system where the influence of a strong atom-cavity coupling and a strong optomechanical interaction are studied. We find a dressed state picture can explain the spectra by predicting the exact peak locations as well as the relative peak heights. In our analysis we also include the effect of mechanical losses (under weak mechanical damping limit) and single-photon loss through spontaneous emission from the two-level emitter

Strong coupling optical spectra in dipole-dipole interacting optomechanical Tavis-Cummings models

We theoretically investigate the emission spectrum of an optomechanical Tavis-Cummings model: two dipole-dipole interacting atoms coupled to an optomechanical cavity (OMC). In particular, we study the influence of dipole-dipole interaction (DDI) on the single-photon spectrum emitted by this hybrid system in the presence of a strong atom-cavity as well as strong optomechanical interaction (hereinafter called the strong-strong coupling). We also show that our analysis is amenable to inclusion of mechanical losses (under the weak mechanical damping limit) and single-photon loss through spontaneous emission from the two-level emitters under a non-local Lindblad model.Comment: 5 pages, 5 figures, Application of non-local Lindblad mode

Controlling tripartite entanglement among optical cavities by reservoir engineering

We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviors indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system resonant frequency. Our scheme shows these effects in the context of optical cavities starting off in a maximally entangled W and Greenberger-Horne-Zeilinger (GHZ) tripartite states. In Lorentzian cases we find that the far detuned double Lorentzian baths with small coupling strengths and for ohmic type baths super-ohmic environments with smaller cutoff frequencies are the best candidates for preserving entanglement among cavities for significant amount of time. A non-Markovian quantum jump approach is employed to understand the entanglement dynamics in these cases, especially to recognize the collapse and revival of the entanglement in both W and GHZ states

On Wave Function Representation of Particles as Shock Wave Discontinuities

In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a non-zero quantum force. The quantum force causes wave packet dispersion which results in the intersection of characteristic curves developing a shock discontinuity. Since quantum force vanishes for localized quantum density waves [1], it is thus established that localized quantum density waves form the only class of wave function representation of particles in quantum theory without shock wave discontinuities.Comment: To appear in Theoretical Physic

Transmission time and resonant tunneling through barriers using localized quantum density soliton waves

In this paper, the interaction and transmission time of quantum density solitons waves representing particles passing through finite barrier potentials is investigated. Using the conservation of energy and of quantum density, it is first demonstrated that these waves have finite de Broglie wavelength and represent particles in quantum theory. The passage of the quantum density solitons (particles) through barriers of finite energies is then shown to lead to the phenomena of resonant tunneling and, in Josephson-like configurations, to the quantization of magnetic flux. A precise general measure for barrier tunneling time is derived which is found to give a new interpretation of the quantum indeterminacy principles

Can accelerated expansion of the universe be due to spacetime vorticity?

We present here a general relativistic mechanism for accelerated cosmic expansion and the Hubble's constant. It is shown that spacetime vorticity coupled to the magnetic field density in galaxies causes the galaxies to recede from one another at a rate equal to the Hubble's constant. We therefore predict an oscillatory universe, with zero curvature, without assuming violation of Newtonian gravity at large distances or invoking dark energy/dark matter hypotheses. The value of the Hubble's constant, along with the scale of expansion, as well as the high isotropy of CMB radiation are deduced from the model.Comment: To appear in Mod. Phys. Lett.

Noncommutative geometry and the classical orbits of particles in a central force potential

We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations $[x_i, x_j]=i \theta_{ij}$. Comparison with observation places severe constraints on the value of the noncommutativity parameter

The Klein-Gordon and the Dirac oscillators in a noncommutative space

We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.Comment: 9 page