Self-consistent methods for interacting lattice bosons with U(1)-symmetry-breaking

This thesis is dedicated to the derivation and benchmarking of self-consistent numerical methods that can be applied to interacting bosonic lattice models. The central goal is to derive methods with low numerical complexity but high accuracy, to be applied to complex systems which are out-of reach for established methods such as path integral quantum Monte Carlo (QMC) or the density matrix renormalization group. In the first part we derive the self-energy functional theory (SFT) for bosons. Building upon previous works on lattice systems without U(1)-symmetry-breaking, we systematically extend SFT to the possibility of a broken U(1)-symmetry and the presence of disorder. SFT incorporates bosonic dynamical mean-field theory as a certain limit, and represents a general non-perturbative framework, enabling the construction of diagrammatically sound approximations in the thermodynamical limit that are controlled in the number of optimization parameters. Using just three variational parameters, we are able to study the Bose-Hubbard model both in its clean version and in the presence of local disorder, showing excellent agreement with numerically exact QMC results. We systematically analyze the corresponding spectral functions, which cannot be fully captured by QMC. In particular, we find that in the presence of disorder the phase transition from the Bose glass to the superfluid phase at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites, leading to a small condensate fraction over a strongly-localized background. The second part is dedicated to the derivation of reciprocal cluster mean-field theory (RCMF) and its application to the strongly-interacting Harper-Hofstadter-Mott model (HHMm). In RCMF the full lattice in the thermodynamical limit is projected onto finite-size clusters, which are decoupled in reciprocal space through a mean-field decoupling approximation, crucially preserving the symmetries of the non-interacting dispersion. The resulting groundstate phase diagram of the HHMm exhibits band insulating, striped superfluid, and supersolid phases. Furthermore, we observe gapless uncondensed liquid phases at integer fillings, and a metastable competing fractional quantum Hall (fQH) phase. The fQH phase, predicted as the groundstate by other methods, is most likely underestimated by RCMF. We then show how a quasi-one-dimensional geometry stabilizes gapped topologically non-trivial groundstates in the HHMm. We observe quasi-one-dimensional analogues of fQH phases at fillings 1/2 and 3/2, and unconventional gapped non-degenerate groundstates at integer filling with quantized Hall responses. By systematically comparing results computed with RCMF and exact diagonalization (ED), we are able to give conclusive quantitative answers on the phase boundaries of the system, as the two methods approach the thermodynamical limit from opposite sides, since RCMF favours gapless and ED gapped phases

Asymptotic safety in higher-derivative gravity

We study the non-perturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The non-perturbative contributions to the $\beta$-functions shift the known perturbative ultraviolet fixed point into a non-trivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.Comment: 8 pages; 1 figure; revised versio

An extension problem for the CR fractional Laplacian

We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.Comment: 33 pages. arXiv admin note: text overlap with arXiv:0709.1103 by other author

Distributed quantum metrology with a single squeezed-vacuum source

We propose an interferometric scheme for the estimation of a linear combination with non-negative weights of an arbitrary number M > 1 of unknown phase delays, distributed across an M-channel linear optical network, with Heisenberg-limited sensitivity. This is achieved without the need of any sources of photon-number or entangled states, photon-number-resolving detectors, or auxiliary interferometric channels. Indeed, the proposed protocol remarkably relies upon a single squeezed-state source, an antisqueezing operation at the interferometer output, and on-off photodetectors

Self-consistent methods for interacting lattice bosons with U(1)-symmetry-breaking

This thesis is dedicated to the derivation and benchmarking of self-consistent numerical methods that can be applied to interacting bosonic lattice models. The central goal is to derive methods with low numerical complexity but high accuracy, to be applied to complex systems which are out-of reach for established methods such as path integral quantum Monte Carlo (QMC) or the density matrix renormalization group. In the first part we derive the self-energy functional theory (SFT) for bosons. Building upon previous works on lattice systems without U(1)-symmetry-breaking, we systematically extend SFT to the possibility of a broken U(1)-symmetry and the presence of disorder. SFT incorporates bosonic dynamical mean-field theory as a certain limit, and represents a general non-perturbative framework, enabling the construction of diagrammatically sound approximations in the thermodynamical limit that are controlled in the number of optimization parameters. Using just three variational parameters, we are able to study the Bose-Hubbard model both in its clean version and in the presence of local disorder, showing excellent agreement with numerically exact QMC results. We systematically analyze the corresponding spectral functions, which cannot be fully captured by QMC. In particular, we find that in the presence of disorder the phase transition from the Bose glass to the superfluid phase at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites, leading to a small condensate fraction over a strongly-localized background. The second part is dedicated to the derivation of reciprocal cluster mean-field theory (RCMF) and its application to the strongly-interacting Harper-Hofstadter-Mott model (HHMm). In RCMF the full lattice in the thermodynamical limit is projected onto finite-size clusters, which are decoupled in reciprocal space through a mean-field decoupling approximation, crucially preserving the symmetries of the non-interacting dispersion. The resulting groundstate phase diagram of the HHMm exhibits band insulating, striped superfluid, and supersolid phases. Furthermore, we observe gapless uncondensed liquid phases at integer fillings, and a metastable competing fractional quantum Hall (fQH) phase. The fQH phase, predicted as the groundstate by other methods, is most likely underestimated by RCMF. We then show how a quasi-one-dimensional geometry stabilizes gapped topologically non-trivial groundstates in the HHMm. We observe quasi-one-dimensional analogues of fQH phases at fillings 1/2 and 3/2, and unconventional gapped non-degenerate groundstates at integer filling with quantized Hall responses. By systematically comparing results computed with RCMF and exact diagonalization (ED), we are able to give conclusive quantitative answers on the phase boundaries of the system, as the two methods approach the thermodynamical limit from opposite sides, since RCMF favours gapless and ED gapped phases

Innovation strategies for education: Liberal and Utilitarian Educational Tendencies in the Higher Education System

This paper discusses innovation strategies for education. The authors of the paper argue that the leading modern universities are the educational and training ones. The global changes in higher education have happened due to several reasons: information playing a key role in modern society (nowadays, it is possible to find plenty of information on any questions); the task of education is to develop educational, professional and cultural skills of students, which is not the original central idea of modern European countries as well as Russia; the tendency to unite several higher education institutions. The authors acknowledge that there are several trends in higher education: the multilevel system; modern information technologies; the distant educational system and development; university complexes; new educational standards; new educational technologies and management structures etc. At the same time, the authors claim that there are at least two systems (tendencies) in the theory of university development: liberal and pragmatic. The former is connected with the educational university’s mission; the later is related to the needs of modern society

Influencia de la combinación de agregado de cerro y de río en la capacidad de soporte de un afirmado

RESUMEN La presente investigación tuvo por objetivo principal determinar la influencia de la combinación de agregado de río y de cerro en la capacidad de soporte de un afirmado, utilizándose para ello 3 combinaciones de agregado de río y agregado de cerro correspondientes a los siguientes porcentajes del 75%/25%, 50%/50%, 25%/75% respectivamente. La investigación se realizó usando agregados de río extraído de la cantera Chonta y agregados de cerro extraído de la cantera Bazán, de los cuales se analizaron sus propiedades físicas y mecánicas dentro de ellas el contenido de humedad, abrasión, granulometría, límites de Atterberg, compactación y CBR; posteriormente se realizaron las combinaciones propuestas de agregado de río y de cerro de las canteras seleccionadas analizándose también sus propiedades físicas y mecánicas dentro de ellas límites de Atterberg, compactación, y CBR. Al procesar los datos de los diferentes ensayos realizados se obtiene que: el agregado de la cantera de río (Chonta) tuvo un CBR de 15% y el agregado de la cantera de cerro (Bazán) tuvo un CBR de 22%, la combinación de: agregado de río / agregado de cerro, para una proporción 75%/25% se obtuvo un CBR 110%, para la proporción 50%/50% se obtuvo un CBR de 55% y para la proporción 25%/75% se obtuvo un CBR de 75%. De los datos obtenidos se puede concluir que ninguna de las canteras cumple con los requisitos mínimos de diseño de afirmado según el Manual de carreteras 2013, mientras que las 3 combinaciones cumplen con lo requerido, indicándose que la proporción 75%/25% tuvo la mejor capacidad de soporte (CBR).ABSTRACT The main objective of the present investigation is to determine the influence of the combination of river and hill aggregate on the support capacity of a firm, using 3 combinations of river aggregate and hill aggregate corresponding to the following percentages of 75% / 25%, 50% / 50%, 25% / 75% respectively. The research was carried out using river aggregates extracted from the Chonta quarry and the aggregates of hills extracted from the Bazán quarry, from which their physical and mechanical properties were analyzed within them the moisture content, abrasion, granulometry, Atterberg limits, compaction And CBR; Later the proposed combinations of river and hill aggregates of the selected quarries were realized, also analyzing their physical and mechanical properties within them limits of Atterberg, compaction, and CBR. When the data of the different tests were processed, it was obtained that: the aggregate of the riverbed (Chonta) had a CBR of 15% and the aggregate of the hill of Bazán had a CBR of 22%, the combination of : River aggregate / hill aggregate, for a ratio of 75% / 25% a CBR 110% was obtained, for the 50% / 50% ratio a CBR of 55% was obtained and for the proportion 25% / 75% was obtained A CBR of 75%. From the data obtained it is possible to conclude that none of the quarries meet the minimum requirements of design of affirmed according to the Road Manual 2013, while the 3 combinations comply with what is required, indicating that the ratio 75% / 25% has the best Carrying capacity (CBR)

Specific binding of the regulatory protein ExpG to promoter regions of the galactoglucan biosynthesis gene cluster of Sinorhizobium meliloti: a combined molecular biology and force spectroscopy investigation

Bartels FW, Baumgarth B, Anselmetti D, Ros R, Becker A. Specific binding of the regulatory protein ExpG to promoter regions of the galactoglucan biosynthesis gene cluster of Sinorhizobium meliloti: a combined molecular biology and force spectroscopy investigation. Journal of structural biology. 2003;143(2):145-152.Specific protein-DNA interaction is fundamental for all aspects of gene transcription. We focus on a regulatory DNA-binding protein in the Gram-negative soil bacterium Sinorhizobium meliloti 2011, which is capable of fixing molecular nitrogen in a symbiotic interaction with alfalfa plants. The ExpG protein plays a central role in regulation of the biosynthesis of the exopolysaccharide galactoglucan, which promotes the establishment of symbiosis. ExpG is a transcriptional activator of exp gene expression. We investigated the molecular mechanism of binding of ExpG to three associated target sequences in the exp gene cluster with standard biochemical methods and single molecule force spectroscopy based on the atomic force microscope (AFM). Binding of ExpG to expA1, expG-expD1, and expE1 promoter fragments in a sequence specific manner was demonstrated, and a 28 bp conserved region was found. AFM force spectroscopy experiments confirmed the specific binding of ExpG to the promoter regions, with unbinding forces ranging from 50 to 165pN in a logarithmic dependence from the loading rates of 70-79000 pN/s. Two different regimes of loading rate-dependent behaviour were identified. Thermal off-rates in the range of k off = (1.2 ± 1.0) × 10 -3 s -1 were derived from the lower loading rate regime for all promoter regions. In the upper loading rate regime, however, these fragments exhibited distinct differences which are attributed to the molecular binding mechanism