A revision of the Generalized Uncertainty Principle

The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant $G_N = L_{Pl}^2$. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg Uncertainty Principle is proportional to the first power of the Planck length $L_{Pl}$. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought.Comment: 6 pages, 1 figur

On the modification of Hamiltonians' spectrum in gravitational quantum mechanics

Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies the Heisenberg uncertainty principle. This modified version is usually called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes all Hamiltonians in quantum mechanics. In this Letter, we use a recently proposed GUP which is consistent with String Theory, Doubly Special Relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. This form of GUP results in two additional terms in any quantum mechanical Hamiltonian, proportional to $\alpha p^3$ and $\alpha^2 p^4$, respectively, where $\alpha \sim 1/M_{Pl}c$ is the GUP parameter. By considering both terms as perturbations, we study two quantum mechanical systems in the framework of the proposed GUP: a particle in a box and a simple harmonic oscillator. We demonstrate that, for the general polynomial potentials, the corrections to the highly excited eigenenergies are proportional to their square values. We show that this result is exact for the case of a particle in a box.Comment: 11 pages, to appear in Europhysics Letter

Brane Cosmology and KK Gravitinos

The cosmology of KK gravitinos in models with extra dimensions is considered. The main result is that the production of such KK modes is not compatible with an epoch of non--standard expansion after inflation. This is so because the BBN constraint on the zero mode forces the reduced five dimensional Planck mass $M_5$ down to values much smaller than the usual four dimensional one, but this in turn implies many KK states available for a given temperature. Once these states are taken into account one finds that there is no $M_5$ for which the produced KK gravitinos satisfy BBN and overclosure constraints. This conclusion holds for both flat and warped models in which only gravity propagates in the full spacetime.Comment: 19 pages, references added, IoP styl

Testing the performance and accuracy of the RELXILL model for the relativistic X-ray reflection from accretion disks

The reflection spectroscopic model RELXILL is commonly implemented in studying relativistic X-ray reflection from accretion disks around black holes. We present a systematic study of the model's capability to constrain the dimensionless spin and ionization parameters from $\sim$6,000 NuSTAR simulations of a bright X-ray source employing the lamppost geometry. We employ high count spectra to show the limitations in the model without being confused with limitations in signal-to-noise. We find that both parameters are well-recovered at 90% confidence with improving constraints at higher reflection fraction, high spin, and low source height. We test spectra across a broad range - first at 10$^6-$10$^7$ and then $\sim$10$^5$ total source counts across the effective 3-79 keV band of NuSTAR, and discover a strong dependence of the results on how fits are performed around the starting parameters, owing to the complexity of the model itself. A blind fit chosen over an approach that carries some estimates of the actual parameter values can lead to significantly worse recovery of model parameters. We further stress on the importance to span the space of nonlinear-behaving parameters like $log~\xi$ carefully and thoroughly for the model to avoid misleading results. In light of selecting fitting procedures, we recall the necessity to pay attention to the choice of data binning and fit statistics used to test the goodness of fit by demonstrating the effect on the photon index $\Gamma$. We re-emphasize and implore the need to account for the detector resolution while binning X-ray data and using Poisson fit statistics instead while analyzing Poissonian data.Comment: 9 pages, 6 figures, accepted for publication in Ap

Asymmetric Properties of Heat Conduction in a One-Dimensional Frenkel-Kontorova Model

In this Letter, we show numerically that the rectifying effect of heat flux in a one-dimensional two-segment Frenkel-Kontorova chain demonstrated in recent literature is merely available under the limit of the weak coupling between the two constituent segments. Surprisingly, the rectifying effect will be reversed when the properties of the interface and the system size change. The two types of asymmetric heat conduction are dominated by different mechanisms, which are all induced by the nonlinearity. We further discuss the possibility of the experimental realization of thermal diode or rectifier devices.Comment: 4 Pages, 4 figure