Generalized su(2)su(2) coherent states for the Landau levels and their nonclassical properties

Following the lines of the recent papers [J. Phys. A: Math. Theor. 44, 495201 (2012); Eur. Phys. J. D 67, 179 (2013)], we construct here a new class of generalized coherent states related to the Landau levels, which can be used as the finite Fock subspaces for the representation of the $su(2)$ Lie algebra. We establish the relationship between them and the deformed truncated coherent states. We have, also, shown that they satisfy the resolution of the identity property through a positive definite measures on the complex plane. Their nonclassical and quantum statistical properties such as quadrature squeezing, higher order `$su(2)$' squeezing, anti-bunching and anti-correlation effects are studied in details. Particularly, the influence of the generalization on the nonclassical properties of two modes is clarified.Comment: arXiv admin note: text overlap with arXiv:1212.6888, arXiv:1404.327

Generalized su(1,1)su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the $su(1,1)$ Lie algebra. This is why we call them the generalized $su(1,1)$ CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.Comment: arXiv admin note: substantial text overlap with arXiv:1212.688

Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field B, respectively, in two dimensional flat surface and an infinite flat band. We explain how these states come directly from the generating functions of the certain families of classical orthogonal polynomials without the complexity of the algebraic approaches. We have shown that some examples become consistent with the Klauder- Perelomove and the Barut-Girardello coherent states. It can be extended to the non-classical, q-orthogonal and the exceptional orthogonal polynomials, too. Especially for physical systems that they don't have a specific algebraic structure or involved with the shape invariance symmetries, too.Comment: 16 page

Thermodynamics of Rotating Black Branes in Gauss-Bonnet-nonlinear Maxwell Gravity

We consider the Gauss-Bonnet gravity in the presence of a new class of nonlinear electromagnetic field, namely, power Maxwell invariant. By use of a suitable transformation, we obtain a class of real rotating solutions with $k$ rotation parameters and investigate some properties of the solutions such as existence of singularity(ies) and asymptotic behavior of them. Also, we calculate the finite action, thermodynamic and conserved quantities of the solutions and using the the Smarr-type formula to check the first law of thermodynamics.Comment: 15 page

Charged Lifshitz Black Holes

We investigate modifications of the Lifshitz black hole solutions due to the presence of Maxwell charge in higher dimensions for arbitrary $z$ and any topology. We find that the behaviour of large black holes is insensitive to the topology of the solutions, whereas for small black holes significant differences emerge. We generalize a relation previously obtained for neutral Lifshitz black branes, and study more generally the thermodynamic relationship between energy, entropy, and chemical potential. We also consider the effect of Maxwell charge on the effective potential between objects in the dual theory.Comment: Latex, 28 pages, 14 figures, some references adde

Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions

We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However a proper analytical solution was not obtain, we try to solve it numerically (by the Runge-Kotta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N=l=b=1, the metric turns to the NUT solution only in 8 dimensions, but in 4 and 6 dimensions the spacetime does not have any Nut solution.Comment: 8 pages, 5 figure