Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states

Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given

Generalized coherent and intelligent states for exact solvable quantum systems

The so-called Gazeau-Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson-Schr\"odinger uncertainty relation. As illustration, the P\"oschl-Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau-Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy

N=2\mathcal{N}=2 Supersymmetry Partial Breaking and Tadpole Anomaly

We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1)$ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint and D3 brane tadpole anomaly of type IIB string on Calabi-Yau threefolds in presence of H$^{RR}$ and H$^{NS}$ fluxes. We also comment on supersymmetry breaking in the particular $\mathcal{N}=2$ $U(1)$ Maxwell theory; and study its interpretation in connection with the tadpole anomaly with extra localized flux sources.Comment: LaTex 37 page

Lie symmetries analysis for SIR model of epidemiology

Abstract In this paper a system of nonlinear ordinary differential equations arising from SIR model of epidemiology is transformed into a system of one equation of second order and one of first order. We use the property of the Lie generators algebras for any two dimensional Lie algebra to solve the first equation of the system. Then, the Lie point symmetry method is applied and differential invariants are used to obtain some exact solutions of the model. Mathematics Subject Classification: 35Bxx, 35Dxx, 92Bx

The Moyal Bracket in the Coherent States framework

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.Comment: 13 page