Study of the Coleman - de Luccia instanton of the second order

We study the second order Coleman - de Luccia instanton which appears as the curvature of the effective potential reaches a sufficiently large value. We show how one can find the approximative formula for this instanton by perturbative expansion in the case when the second derivative of the effective potential divided by the Hubble parameter squared is close to -10, and we perform a numerical study of this instanton in the case of quasi-exponential potential.Comment: three pages, one figur

Commutator Anomaly in Noncommutative Quantum Mechanics

In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.Comment: 7 page

Coleman - de Luccia instanton of the second order in a brane world

The second order Coleman - de Luccia instanton and its action in the Randall - Sundrum type II model are investigated and the comparison with the results in Einstein's general relativity is done in the present paper.Comment: 4 pages, accepted in IJT

Bound state energies and phase shifts of a non-commutative well

Non-commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non-commutative configuration space. Within this framework an unambiguous definition can be given for the non-commutative well. Using this approach we compute the bound state energies, phase shifts and scattering cross sections of the non- commutative well. As expected the results are very close to the commutative results when the well is large or the non-commutative parameter is small. However, the convergence is not uniform and phase shifts at certain energies exhibit a much stronger then expected dependence on the non-commutative parameter even at small values.Comment: 12 pages, 8 figure

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.Comment: minor changes done, references added, version to appear in GR

The HMW effect in Noncommutative Quantum Mechanics

The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.Comment: 8 Latex page

Weyl-Wigner Formulation of Noncommutative Quantum Mechanics

We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Seiberg-Witten map we construct an isomorphism between the operator and the phase space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended starproduct, Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of Seiberg-Witten map. Our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some 2-dimensional spaces.Comment: Revtex4, 3 diagrams, 32 page

False vacuum decay with gravity in a critical case

The vacuum decay in a de Sitter universe is studied within semiclassical approximation for the class of effective inflaton potentials whose curvature at the top is close to a critical value. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined. The case when the fourth derivative of the effective potential at its top is less than a critical value is discussed.Comment: 10 pages, 8 figures, minor changes don

Noncommutative quantum mechanics and Bohm's ontological interpretation

We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing

Impact of Intermediate Hyperglycemia and Diabetes on Immune Dysfunction in Tuberculosis

Supplementary Data: Supplementary materials are available at Clinical Infectious Diseases online at https://academic.oup.com/cid/article/72/1/69/5857148#274319223 . Consisting of data provided by the authors to benefit the reader, the posted materials are not copyedited and are the sole responsibility of the authors, so questions or comments should be addressed to the corresponding author.Copyright © The Author(s) 2020. Background: People with diabetes have an increased risk of developing active tuberculosis (TB) and are more likely to have poor TB-treatment outcomes, which may impact on control of TB as the prevalence of diabetes is increasing worldwide. Blood transcriptomes are altered in patients with active TB relative to healthy individuals. The effects of diabetes and intermediate hyperglycemia (IH) on this transcriptomic signature were investigated to enhance understanding of immunological susceptibility in diabetes-TB comorbidity. Methods: Whole blood samples were collected from active TB patients with diabetes (glycated hemoglobin [HbA1c] ≥6.5%) or IH (HbA1c = 5.7% to <6.5%), TB-only patients, and healthy controls in 4 countries: South Africa, Romania, Indonesia, and Peru. Differential blood gene expression was determined by RNA-seq (n = 249). Results: Diabetes increased the magnitude of gene expression change in the host transcriptome in TB, notably showing an increase in genes associated with innate inflammatory and decrease in adaptive immune responses. Strikingly, patients with IH and TB exhibited blood transcriptomes much more similar to patients with diabetes-TB than to patients with only TB. Both diabetes-TB and IH-TB patients had a decreased type I interferon response relative to TB-only patients. Conclusions: Comorbidity in individuals with both TB and diabetes is associated with altered transcriptomes, with an expected enhanced inflammation in the presence of both conditions, but also reduced type I interferon responses in comorbid patients, suggesting an unexpected uncoupling of the TB transcriptome phenotype. These immunological dysfunctions are also present in individuals with IH, showing that altered immunity to TB may also be present in this group. The TB disease outcomes in individuals with IH diagnosed with TB should be investigated further.European Union’s Seventh Framework Programme (FP7 2007-2013 - Health) under grant agreement No 305279