Localization Lifetime of a Many-Body System with Periodic Constructed Disorder

We show that, in a many-body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time-domain formulation is complementary to the formulation of the many-body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one-dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations

On total reality of meromorphic functions

We show that if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points then it is conjugate to a real meromorphic function after a suitable projective automorphism of the image.Comment: 13 page

The anomaly-induced effective action and natural inflation

The anomaly-induced inflation (modified Starobinsky model) is based on the application of the effective quantum field theory approach to the Early Universe. We present a brief general review of the model and show that it does not require a fine-tuning for the parameters of the theory or initial data, gives a real chance to meet a graceful exit to the FRW phase and also has positive features with respect to the metric perturbations.Comment: Invited talk at the International Workshop on Astroparticle and High Energy Physics, October 14 - 18, 2003, Valencia, Spai

RNA Sequencing Reveals a Role of TonEBP Transcription Factor in Regulation of Pro-inflammatory Genes in Response to Hyperosmolarity in Healthy Nucleus Pulposus Cells: A HOMEOSTATIC RESPONSE?

Transcription factor tonicity-responsive enhancer-binding protein (TonEBP/NFAT5) is critical for osmo-adaptation and extracellular matrix homeostasis of nucleus pulposus (NP) cells in their hypertonic tissue niche. Recent studies implicate TonEBP signaling in inflammatory disease and rheumatoid arthritis pathogenesis. However, broader functions of TonEBP in the disc remain unknown. RNA sequencing was performed on NP cells with TonEBP knockdown under hypertonic conditions. 1140 TonEBP-dependent genes were identified and categorized using Ingenuity Pathway Analysis. Bioinformatic analysis showed enrichment of matrix homeostasis and cytokine/chemokine signaling pathways. C-C motif chemokine ligand 2 (CCL2), interleukin 6 (IL6), tumor necrosis factor (TNF), and nitric oxide synthase 2 (NOS2) were studied further. Knockdown experiments showed that TonEBP was necessary to maintain expression levels of these genes. Gain- and loss-of-function experiments and site-directed mutagenesis demonstrated that TonEBP binding to a specific site in the CCL2 promoter is required for hypertonic inducibility. Despite inhibition by dominant-negative TonEBP, IL6 and NOS2 promoters were not hypertonicity-inducible. Whole-disc response to hypertonicity was studied in an ex vivo organ culture model, using wild-type and haploinsufficient TonEBP mice. Pro-inflammatory targets were induced by hypertonicity in discs from wild-type but not TonEBP-haploinsufficient mice. Mechanistically, NF-κB activity increased with hypertonicity and was necessary for hypertonic induction of target genes IL6, TNF, and NOS2 but not CCL2 Although TonEBP maintains transcription of genes traditionally considered pro-inflammatory, it is important to note that some of these genes also serve anabolic and pro-survival roles. Therefore, in NP cells, this phenomenon may reflect a physiological adaptation to diurnal osmotic loading of the intervertebral disc

Expansion of a Bose-Einstein Condensate in the Presence of Disorder

Expansion of a Bose-Einstein condensate (BEC) is studied, in the presence of a random potential. The expansion is controlled by a single parameter, $(\mu\tau_{eff} /\hbar)$, where $\mu$ is the chemical potential, prior to the release of the BEC from the trap, and $\tau_{eff}$ is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location

Vacuum effective action and inflation

We consider vacuum quantum effects in the Early Universe, which may lead to inflation. The inflation is a direct consequence of the supposition that, at high energies, all the particles can be described by the weakly interacting, massless, conformally invariant fields. We discuss, from the effective field theory point of view, the stability of inflation, transition to the FRW solution, and also possibility to study metric and density perturbations.Comment: 6 pages, LaTeX, no figures. Contribution to the Proceedings of the X Jorge Andre Swieca school in Particles and Fields. To be published in World Scientifi