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Register a new userDeformed dispersion relations and the degree of coherence function
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The analysis of the modifications that the presence of a deformed dispersion relation entails in the roots of the so--called degree of coherence function, for a beam embodying two different frequencies and moving in a Michelson interferometer, is carried out. The conditions to be satisfied, in order to detect this kind of quantum gravity effect, are also obtained.
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Following the methods developed by Corley and Jacobson, we consider qualitatively the issue of Hawking radiation in the case when the dispersion relation is dictated by quantum kappa-Poincare algebra. This relation corresponds to field equations that are non-local in time, and, depending on the sign of the parameter kappa, to sub- or superluminal signal propagation. We also derive the conserved inner product, that can be used to count modes, and therefore to obtain the spectrum of black hole radiation in this case.
We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist $-$giving $kappa$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lema^{i}tre-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lema^itre-Robertson-Walker (FLRW) geometry that is locally identical to the $kappa$-Poincare dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such Hamiltonian we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe.
Generalized coherent states (GCs) under deformed quantum mechanics which exhibits intrinsic minimum length and maximum momentum have been well studied following Gazeau-Klauder approach. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schrodinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schrodinger cat states (GKSCs), 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. Non-classical properties of the deformed-GKSCs are explored in terms of Mandel Q parameter, quadrature squeezing as well as Husimi quasi-probability distribution. 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 describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $kappa$-Poincare quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
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