Horizon wave-function for single localized particles: GUP and quantum black hole decay

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.Comment: 8 pages, 5 figures, extended version of arXiv:1305.3195 with new results about the GUP and black hole decay, clarifications about black hole decay adde

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.Comment: 9 page

Natural extension of the Generalised Uncertainty Principle

We discuss a gedanken experiment for the simultaneous measurement of the position and momentum of a particle in de Sitter spacetime. We propose an extension of the so-called generalized uncertainty principle (GUP) which implies the existence of a minimum observable momentum. The new GUP is directly connected to the nonzero cosmological constant, which becomes a necessary ingredient for a more complete picture of the quantum spacetime.Comment: 4 pages, 1 figure, v2 with added references, revised and extended as published in CQ

Stellar turbulent convection: the multiscale nature of the solar magnetic signature

The multiscale dynamics associated with turbulent convection present in physical systems governed by very high Rayleigh numbers still remains a vividly disputed topic in the community of astrophysicists, and in general, among physicists dealing with heat transport by convection. The Sun is a very close star for which detailed observations and estimations of physical properties on the surface, connected to the processes of the underlying convection zone, are possible. This makes the Sun a unique natural laboratory in which to investigate turbulent convection in the hard turbulence regime, a regime typical of systems characterized by high values of the Rayleigh number. In particular, it is possible to study the geometry of convection using the photospheric magnetic voids (or simply voids), the quasi-polygonal quiet regions nearly devoid of magnetic elements, which cover the whole solar surface and which form the solar magnetic network. This work presents the most extensive statistics, both in the spatial scales studied (1-80 Mm) and in the temporal duration (SC 23 and SC 24), to investigate the multiscale nature of solar magnetic patterns associated with the turbulent convection of our star. We show that the size distribution of the voids, in the 1-80 Mm range, for the 317, 870 voids found in the 692 analyzed magnetograms, is basically described by an exponential function

Black hole thermodynamics with generalized uncertainty principle

In the standard viewpoint, the temperature of a stationary black hole is proportional to its surface gravity, $T_H=\hbar\kappa/2\pi$. This is a semiclassical result and the quantum gravity effects are not taken into consideration. This Letter explores a unified expression for the black hole temperature in the sense of a generalized uncertainty principle(GUP). Our discussion involves a heuristic analysis of a particle which is absorbed by the black hole. Besides a class of static and spherically symmetric black holes, an axially symmetric Kerr-Newman black hole is considered. Different from the existing literature, we suggest that the black hole's irreducible mass represent the characteristic size in the absorption process. The information capacity of a remnant is also discussed by Bousso's D-bound in de Sitter spacetime.Comment: 18 pages, great improvement on the first version; a Kerr-Newman black hole is considere

Some Aspects of Minimal Length Quantum Mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.Comment: 9 pages, one eps figur

Quality control and analytical test method for Taxus baccata tincture preparation.

The homeopathic tincture of Taxus baccata L. is monographed in the current German Homeopathic Pharmacopoeia (HAB 2009). However, the described identification test is a common comparative TLC procedure that might be updated. The purpose of the current work was the quali-quantitative analysis by HPLC/DAD/MS of Taxus tincture. In this study we characterized polyphenolic compounds, in particular four hydroxycinnamic derivatives (0.85 mg/mL) and four flavonoids (quercetin and kaempferol 3- O-rutinoside and xylosyl glucosides); the total polyphenol content was 1.265 mg/mL of tincture. Starting from the official German Homeopathic Pharmacopoeia method of preparation, the aim of this work was to optimize a rapid and reproducible method for the analysis of herbal drugs and tincture, directly prepared in store or the herbalist's shop, to ensure safety and efficacy of the preparation. The procedure has to ensure validation, robustness of the results, and provide a quick response about the composition of compounds in the herbal drug preparation

Minimum black hole mass from colliding Gaussian packets

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in details, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.Comment: 11 pages, 4 figure