The continuum limit of a 4-dimensional causal set scalar d'Alembertian

The continuum limit of a 4-dimensional, discrete d'Alembertian operator for scalar fields on causal sets is studied. The continuum limit of the mean of this operator in the Poisson point process in 4-dimensional Minkowski spacetime is shown to be the usual continuum scalar d'Alembertian $\Box$. It is shown that the mean is close to the limit when there exists a frame in which the scalar field is slowly varying on a scale set by the density of the Poisson process. The continuum limit of the mean of the causal set d'Alembertian in 4-dimensional curved spacetime is shown to equal $\Box - \frac{1}{2}R$, where $R$ is the Ricci scalar, under certain conditions on the spacetime and the scalar field.Comment: 31 pages, 2 figures. Slightly revised version, accepted for publication in Classical and Quantum Gravit

The effects of high dose vitamin D supplementation on glucose metabolism and inflammation in obese adolescents

Title from PDF of title page (University of Missouri--Columbia, viewed on May 29, 2013).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Thesis advisor: Dr. Catherine A. PetersonIncludes bibliographical references.M.S. University of Missouri--Columbia 2012."May 2012"Purpose: The primary aim of this study was to determine the effects of improving vitamin D status through daily supplementation of 4000 IU would improve markers of glucose metabolism and inflammation in obese adolescents. Methods: (age=14.2[plus or minus]2.6 years; BMI=39.2[plus or minus]5.9) were recruited from the University of Missouri-Adolescent Diabetes and Obesity clinic and were randomized to receive either placebo or vit D3 (4000 IU/day) as part of their standard treatment for 6 months. Results: After six months, subjects supplemented with vitamin D3 had significant changes in serum 25-hydroxyvitamin D concentrations (19.4 vs 3.8 ng/ml for placebo; P<0.001), HOMA-IR (-1.63 vs +0.27 for placebo; P=0.026) and QUICKI (+0.016 vs -0.004; P=.016). Additionally, the leptin:adiponectin ratio was reduced in vitamin D group versus placebo (-1.41 vs +0.10 P=0.45). No significant changes from baseline in inflammatory markers were detected between groups. Conclusions: Correcting the poor vitamin D status associated with obesity may be an effective and inexpensive adjuvant to treatment of obesity-related metabolic complications

Exploring spacetime phenomenology: from Lorentz violations to experimental tests of non-locality

This thesis deals primarily with the phenomenology associated to quantum aspects of spacetime. In particular, it aims at exploring the phenomenological consequences of a fundamental discreteness of the spacetime fabric, as predicted by several quantum gravity models and strongly hinted by many theoretical insights. The first part of this work considers a toy-model of emergent spacetime in the context of analogue gravity. The way in which a relativistic Bose\u2013 Einstein condensate can mimic, under specific configurations, the dynamics of a scalar theory of gravity will be investigated. This constitutes proof-ofconcept that a legitimate dynamical Lorentzian spacetime may emerge from non-gravitational (discrete) degrees of freedom. Remarkably, this model will emphasize the fact that in general, even when arising from a relativistic system, any emergent spacetime is prone to show deviations from exact Lorentz invariance. This will lead us to consider Lorentz Invariance Violations as first candidate for a discrete spacetime phenomenology. Having reviewed the current constraints on Lorentz Violations and studied in depth viable resolutions of their apparent naturalness problem, the second part of this thesis focusses on models based on Lorentz invariance. In the context of Casual Set theory, the coexistence of Lorentz invariance and discreteness leads to an inherently nonlocal scalar field theory over causal sets well approximating a continuum spacetime. The quantum aspects of the theory in flat spacetime will be studied and the consequences of its non-locality will be spelled out. Noticeably, these studies will lend support to a possible dimensional reduction at small scales and, in a classical setting, show that the scalar field is characterized by a universal nonminimal coupling when considered in curved spacetimes. Finally, the phenomenological possibilities for detecting this non-locality will be investigated. First, by considering the related spontaneous emission of particle detectors, then by developing a phenomenological model to test nonlocal effects using opto-mechanical, non-relativistic systems. In both cases, one could be able to cast in the near future stringent bounds on the non-locality scale

Quantum Superposition of Massive Objects and the Quantization of Gravity

We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.Comment: 9 pages, 1 figure. Version accepted for publication in Phys.Rev.

Information Content of the Gravitational Field of a Quantum Superposition

When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no ``gravitons'' are emitted during the experiment.Comment: 4 pages, 1 figure. First prize essay in the Gravity Research Foundation 2019 Essays on Gravitation. To appear in IJMPD. arXiv admin note: substantial text overlap with arXiv:1807.0701

Informational steady-states and conditional entropy production in continuously monitored systems

We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady-states (ISSs), i.e. stationary states of a conditional dynamics that are maintained owing to the unbroken acquisition of information. We illustrate the applicability of our framework through several examples

Optomechanics-based quantum estimation theory for collapse models

We make use of the powerful formalism of quantum parameter estimation to assess the characteristic rates of a Continuous Spontaneous Localisation (CSL) model affecting the motion of a massive mechanical system. We show that a study performed in non-equilibrium conditions unveils the advantages provided by the use of genuinely quantum resources -- such as quantum correlations -- in estimating the CSL-induced diffusion rate. In stationary conditions, instead, the gap between quantum performance and a classical scheme disappears. Our investigation contributes to the ongoing effort aimed at identifying suitable conditions for the experimental assessment of collapse models.Comment: 7 pages, 3 figure

Open Quantum Rotors: Connecting Correlations and Physical Currents

We consider a finite one-dimensional chain of quantum rotors interacting with a set of thermal baths at different temperatures. When the interaction between the rotors is made chiral, such a system behaves as an autonomous thermal motor, converting heat currents into non-vanishing rotational ones. Such a dynamical response is strongly pronounced in the range of the Hamiltonian parameters for which the ground state of the system in the thermodynamic limit exhibits a quantum phase transition. Such working points are associated with large quantum coherence and multipartite quantum correlations within the state of the system. This suggests that the optimal operating regime of such quantum autonomous motor is one of maximal quantumness.Comment: 9 pages, 9 figures; comments welcome