No abstract

Generalized coherent states (GCs) under deformed quantum mechanics which exhibit intrinsic minimum length and maximum momentum have been well studied following Gazeau-Klauder approach in Refs. [1][2][3][4]. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schrödinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schrödinger cat states (GKSCs) in [5], we construct the deformed-GKSCs for both phenomenological models that exhibit intrinsic minimum length and/or maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd states statistical properties. Nonclassical properties of the deformed-GKSCs are explored in terms of Mandel Q parameter, quadrature squeezing (∆X q ) · (∆Y q ) as well as Husimi quasi-probability distribution Q. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.

We examine the nonperturbative effect of instrinsic maximum momentum on the relativistic wave equations. Using the momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and Dirac oscillator. Similar to the undeformed case, bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have relevant applications in quarkonium confinement and quantum gravity phenomenology.

We show that a passing gravitational wave may influence the spin entropy and spin negativity of a system of N massive spin-1/2 particles, in a way that is characteristic of the radiation. We establish the specific conditions under which this effect may be nonzero. The change in spin entropy and negativity, however, is extremely small. Here, we propose and show that this effect may be amplified through entanglement swapping. Relativistic quantum information theory may have a contribution towards the detection of gravitational wave.

We will examine the Bianchi Type I universe under the Rainbow Gravity formalism and calculate various quantities like the dynamical equation for the energy density and the negative energy density. Finally, we apply the analysis to a specific Rainbow Gravity model.