Thermodynamics of Quasi-Topological Cosmology

In this paper, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, $r_{+}$, with the apparent horizon radius, $\tilde{r}_{A}$, we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which show the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology.Comment: 8 pages, no figure, Phys. Lett B, in press (2013

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