Midisuperspace foam and the cosmological constant

Wheeler's conjectured "spacetime foam" -- large quantum fluctuations of spacetime at the Planck scale -- could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ``foamy'' initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

On the experiment-friendly formulation of quantum backflow

In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of quantum backflow to situations in which the particle's state may have both positive and negative momenta. Here, we investigate how the experiment-friendly formulation of quantum backflow compares to the standard one when applied to a free particle in a positive-momentum state. We show that the two formulations are not always compatible. We further identify a parametric regime in which the two formulations appear to be in qualitative agreement with one another.

Experiment-friendly formulation of quantum backflow

Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for arbitrary momentum distributions, paving the way towards its experimental verification. We give examples of backflow in gravitational and harmonic potential, and discuss experimental procedures required for the demonstration using atomic gravimeters. Such an experiment would show that the probability of finding a free falling particle above initial level could grow for suitably prepared quantum state with most momentum downwards.

Continuity Relations, Probability Acceleration Current Sources and Internal Communications in Interacting Fragments

Classical issues of local continuities and density partition in molecular quantum mechanics are reexamined. An effective velocity of the probability current is identified as the current-per-particle and its properties are explored. The local probability acceleration and the associated force concept are introduced. They are shown to identically vanish in the stationary electronic states. This acceleration measure also determines the associated productions of physical currents, e.g., the local source of the resultant content of electronic gradient information. The probability partitioning between reactants is revisited and illustrated using the stockholder division rule of Hirshfeld. A simple orbital model is used to describe the polarized (disentangled) and equilibrium (entangled) molecular fragments containing the distinguishable and indistinguishable groups of electrons, respectively, and their mixed quantum character is emphasized. The fragment density matrix is shown to determine the subsystem internal electron communications.

An infinite square-well potential as a limiting case of a square-well potential in a minimal-length scenario

One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well fixed. In order to avoid this we solve the finite square-well potential whose the boundary conditions are well fixed, even in a minimal-length scenario, and then we take the limit of the potential going to infinity to find the eigenfunctions and the energy equation for the infinite square-well potential. Although the first correction for the energy eigenvalues is the same as one found in the literature, our result shows that the eigenfunctions have the first derivative continuous at the square-well walls what is in disagreement with those previous work. That is because in the literature the authors have neglected the hyperbolic solutions and have assumed the discontinuity of the first derivative of the eigenfunctions at the walls of the infinite square-well which is not correct. As we show, the continuity of the first derivative of the eigenfunctions at the square-well walls guarantees the continuity of the probability current density and the unitarity of the time evolution operator.

EL ROSTRO POBRE DE LA DIABETES EN MÉXICO

<p align="center"><strong>RESUMEN</strong><strong></strong></p><p>El objetivo de este documento es modelar la dinámica de las privaciones sociales (PS) de la población carente en México con el fin de diferenciar sus condiciones materiales de vida en presencia o no de diabetes mellitus 2 (DM2). La idea es ofrecer evidencia sobre la influencia que tienen algunos factores económicos y sociales comunitarios en la cadena de causas que condicionan el desarrollo de la DM2 entre los pobres. Para tal efecto, probamos la hipótesis de que la probabilidad de experimentar PS en la población carente es mayor en los individuos que padecen DM2 según sean los tipos de localidades, PS y factores de riesgo clínico considerados. Los resultados obtenidos con un modelo de Markov oculto apoyan la hipótesis de que una parte de la población pobre, que es rural y diabética, es la que tiene más probabilidad actual y futura de experimentar privaciones sociales en México.</p><p> </p><p align="center">THE POOR FACE OF DIABETES IN MEXICO</p><p align="center"><strong>ABSTRACT</strong><strong></strong></p><p>This paper aims at modeling the dynamics of social deprivations (SD) of the Mexican poor population in order to differentiate their material living conditions in the presence or absence of diabetes mellitus 2 (DM2). The idea is to offer evidence on the influence of some community economic and social factors in the chain of causes conditioning the development of DM2 among the poor. For this purpose, we hypothesize that the probabilities of experiencing SD in the Mexican population are higher in individuals with DM2 depending on the type of localities, SD and clinical risk factors considered. The main results drawn from a hidden Markov model support the hypothesis that a part of the poor population, which is rural and diabetic, is the one with the highest probability (current and future) of experiencing sd in Mexico.</p>

Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.