Trapped surfaces and emergent curved space in the Bose-Hubbard model

A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, fall-off of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.Comment: 16 pages two columns, 12 figures; references added, typos correcte

Evaluation of proprioception and postural control at a minimum 1 year follow-up after ankle capsuloligamentous lateralplasty with Brostrom technique: A cohort study

Recovery of postural control and proprioception in patients affected by chronic ankle instability (CAI) and operated on capsulo-ligaments reconstructive surgery lacks of objective assessment. The aim of this study was to evaluate long-term post-surgical postural and proprioceptive control through the DPPS device in a cohort of patients operated on ligaments reconstruction through the modified Brostrom procedure at a minimum follow up of 12 months.Eleven patients with post-traumatic lateral CAI, operated of external capsulo-ligamentous complex repair according to Brostrom technique at a minimum follow-up of 1 year were enrolled. Physical examination and American Orthopaedics Foot and Ankle Society (AOFAS) ankle-hindfoot score. Proprioceptive and postural stability was assessed by DPPS - Delos Postural Proprioceptive System, linked to a computer with a specific software and including a flat table, an electronic unstable proprioceptive board, a Delos Vertical Controller, a monitor and a horizontal bar fitted with an infra-red sensor for hand support.Patients were 5 males and 6 females, mean age of 38.4 ± 12 years. Mean BMI of the patients was 26.8 ± 4.4. Mean follow up was 13.4 ± 2.1. The mean value of (AOFAS) clinical score was 90.3/100. Mean Static Stability Index (SSI) with open eyes was 87.7% (±7.6) in the operated leg and 90.4% (±6.1) in the contra-lateral. SSI with closed eyes was 64.5% (±11.2) in the operated leg and 61.6% (±16.8) in the contra-lateral. Mean Dynamic Stability Index (DSI) without restrictions was 56.2% (±14.6) in the operated leg and 56.8% (±10.6) in the contra-lateral. DSI with restricted upper limbs, had a mean value of 56.3% (±11.4) in the operated leg and 58.1% (±11.9) in the contra-lateral.Re-tensioning capsular-ligamentous surgery of the external compartment for CAI allow to recovery proprioceptive and postural control on the operated side, comparable with data from the contralateral limb and from the healthy population of the same age and sex

Weight bearing versus conventional CT for the measurement of patellar alignment and stability in patients after surgical treatment for patellar recurrent dislocation

Purpose: To compare weight-bearing cone-beam computer tomography (CBCT) and conventional computer tomography (CT)-based measurements of patellofemoral alignment and stability in patients surgically treated for recurrent patellar dislocation. These scans implied respectively single-leg up-right posture, the knee flexed, and lower limb muscles activation, versus supine position with the knee extended. Methods: A total of 17 patients (11 males/6 females) after surgical reconstruction with fascia lata allograft for recurrent patellofemoral dislocation were analyzed at 60-month follow-up. Tilt and congruence angles and tibial tuberosity–trochlear groove (TT-TG) offset were measured on images obtained from CBCT and conventional CT scans by three independent and expert radiologists. Paired t tests were performed to compare measurements obtained from the two scans. Inter-rater reliability was assessed using a two-way mixed-effects model intra-class correlation coefficient (ICC). Results: Only TT-TG offset was found significantly smaller (p < 0.001) in CBCT (mean 9.9 ± 5.3 mm) than in conventional CT (mean 15.9 ± 4.9 mm) scans. ICC for tilt and congruence angles and for TT-TG offset ranged between 0.80–0.94 with measurements in CBCT scans, between 0.52 and0.78 in conventional CT. Conclusion: In patients surgically treated for recurrent patellar dislocation, TT-TG offset was found overestimated with conventional CT. All measurements of patellofemoral stability and alignment were found more consistent when obtained with weight-bearing CBCT compared to conventional CT

Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model

In Verlinde's entropic force scenario of gravity, Newton's laws and Einstein equations can be obtained from the first pinciples and general assumptions. However, the equipartition law of energy is invalid at very low temperatures. We show clearly that the threshold of the equipartition law of energy is related with horizon of the universe. Thus, a one-dimension Debye (ODD) model in the direction of radius of the modified entropic force (MEF) maybe suitable in description of the accelerated expanding universe. We present a Friedmann cosmic dynamical model in the ODD-MEF framework. We examine carefully constraints on the ODD-MEF model from the Union2 compilation of the Supernova Cosmology Project (SCP) collaboration, the data from the observation of the large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the model parameters $\zeta\simeq10^{-9}$ and $\Omega_{m0}=0.224$, with $\chi_{min}^2=591.156$. The corresponding age of the universe agrees with the result of D. Spergel {\it et al.}\cite{Spergel2003} at 95% confidence level. The numerical result also yields an accelerated expanding universe without invoking any kind of dark energy. Taking $\zeta(\equiv 2\pi \omega_D/H_0)$ as a running parameter associated with the structure scale $r$, we obtain a possible unified scenario of the asymptotic flatness of the radial velocity dispersion of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11 anomaly in the entropic force framework of Verlinde.Comment: 23 pages, 6 figure

Gravity from the entropy of light

The holographic principle, considered in a semiclassical setting, is shown to have direct consequences on physics at a fundamental level. In particular, a certain relation is pointed out to be the expression of holography in basic thermodynamics. It is argued moreover that through this relation holography can be recognized to induce gravity, and an expression for the gravitational lensing is obtained in terms of entropy over wavelength of black-body radiation, or, at a deeper level, in terms of maximum entropy over associated space to the elementary bit of information.Comment: 7 pages; v2: completion of the list of references; v3: the discussion is divided in Sections and the argument is described in more detail; v4: a statement is added (below eq.13) on what is the supposed difference between Jacobson's work in ref.21 and this attempt; addition of a paragraph in last Sectio

A Note on Temperature and Energy of 4-dimensional Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be written as $F=\frac{GmM_0}{r^2}$, which could be tested by experiments.Comment: V4: 13 pages, 4 figures, title changed, discussions for experiments added, accepted by CQ

Tibiotalocalcaneal arthrodesis in a rare case of tuberculosis of the talus

Aim To assess our personal experience of a case of tuberculosis of the talus, and to provide an overview of the literature about this tuberculosis manifestations, including all its aspects: epidemiology, clinical and imaging presentation, and all the treatments available to the current state of knowledge. Methods We present our experience in a case of a 34-year-old patient, who came to our attention with difficulty in walking and pain due to a talar tuberculosis, with consequent bone disruption and reabsorption, and foot deformities. Results A tibiotalocalcaneal arthrodesis with retrograde nail and bone graft was performed after antibiotic therapy. Today, almost two years after treatment, the patient can walk independently with no major limitations in everyday life. Conclusion Tibiotalocalcaneal arthrodesis with bone graft showed good functional results in this case study, with complete graft fusion and good functional and radiological outcomes

Thermodynamics in f(R)f(R) gravity in the Palatini formalism

We investigate thermodynamics of the apparent horizon in $f(R)$ gravity in the Palatini formalism with non-equilibrium and equilibrium descriptions. We demonstrate that it is more transparent to understand the horizon entropy in the equilibrium framework than that in the non-equilibrium one. Furthermore, we show that the second law of thermodynamics can be explicitly verified in both phantom and non-phantom phases for the same temperature of the universe outside and inside the apparent horizon.Comment: 20 pages, no figure, accepted in JCA

Spinning Loop Black Holes

In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman-Janis transformation and we specialize to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that the space-times obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation move, if any, the causality violating regions of the Kerr metric far from r=0. We study the space-time structure with particular attention to the horizons shape. We conclude the paper with a discussion on a regular Reissner-Nordstrom black hole derived from the Schwarzschild LBH and then applying again the Newmann-Janis transformation.Comment: 18 pages, 18 figure