2,081 research outputs found
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, , with the apparent horizon radius, , 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 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 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 `' 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 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 Lie algebra. This is why we
call them the generalized 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
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