Related papers: Horizon Quantum Mechanics for spheroidal sources
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a…
Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…
We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of…
We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…
The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum…
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle…
A class of anisotropic Einstein metrics is presented. These metrics are axial symmetric and contains an anisotropy parameter $\alpha$, which is identified as the amplitude of the proper acceleration of the origin, thus explaining the…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
In this paper we start a global study of the parameter space (dissipation, perturbation, frequency) of the dissipative spin-orbit problem in Celestial Mechanics with the aim of delimiting regions where the dynamics, or at least some of its…