Two-body bound and edge states in the extended SSH Bose-Hubbard model

We study the bosonic two-body problem in a Su-Schrieffer-Heeger dimerized chain with on-site and nearest-neighbor interactions. We find two classes of bound states. The first, similar to the one induced by on-site interactions, has its center of mass on the strong link, whereas the second, existing only thanks to nearest-neighbors interactions, is centered on the weak link. We identify energy crossings between these states and analyse them using exact diagonalization and perturbation theory. In the presence of open boundary conditions, novel strongly-localized edge-bound states appear in the spectrum as a consequence of the interplay between lattice geometry, on-site and nearest-neighbor interactions. Contrary to the case of purely on-site interactions, such EBS persist even in the strongly interacting regime.Comment: 12 pages, 8 figures; Submitted to EPJ Special Topics, Quantum Gases and Quantum Coherenc

Turbulent heat transfer in spacer-filled channels: Experimental and computational study and selection of turbulence models

Heat transfer in spacer-filled channels of the kind used in Membrane Distillation was studied in the Reynolds number range 100–2000, encompassing both steady laminar and early-turbulent flow conditions. Experimental data, including distributions of the local heat transfer coefficient h, were obtained by Liquid Crystal Thermography and Digital Image Processing. Alternative turbulence models, both of first order (k-ε, RNG k-ε, k-ω, BSL k-ω, SST k-ω) and of second order (LRR RS, SSG RS, ω RS, BSL RS), were tested for their ability to predict measured distributions and mean values of h. The best agreement with the experimental results was provided by first-order ω-based models able to resolve the viscous/conductive sublayer, while all other models, and particularly ε-based models using wall functions, yielded disappointing predictions

Particle-hole character of the Higgs and Goldstone modes in strongly-interacting lattice bosons

We study the low-energy excitations of the Bose-Hubbard model in the strongly-interacting superfluid phase using a Gutzwiller approach and extract the single-particle and single-hole excitation amplitudes for each mode. We report emergent mode-dependent particle-hole symmetry on specific arc-shaped lines in the phase diagram connecting the well-known Lorentz-invariant limits of the Bose-Hubbard model. By tracking the in-phase particle-hole symmetric oscillations of the order parameter, we provide an answer to the long-standing question about the fate of the pure amplitude Higgs mode away from the integer-density critical point. Furthermore, we point out that out-of-phase oscillations are responsible for a full suppression of the condensate density oscillations of the gapless Goldstone mode. Possible detection protocols are also discussed.Comment: 6 pages, 3 figure

Human capital and convergence:Ttheory, estimation and applications.

In growth theory, convergence analysis tries to answer three fundamental questions "Are poor countries catching up with richer ones How quickly And what are the determinants of this process" This thesis deals with issues that are relevant to all these questions. It begins by setting out the key theoretical contributions to the analysis of the role of human capital in growth and convergence. Secondly, attention is turned to the way that convergence is estimated from data. The econometric techniques used in the convergence literature usually assume that shocks are uncorrelated across countries. We claim that this is unlikely for most data sets and investigate the use of an estimator so far ignored, namely the annual panel estimator where shocks are allowed to be correlated. Our analysis indicates that this estimator is more efficient than conventional ones for plausible values of cross-country error correlation. The study then turns to the analysis of the third question. Although differences in human capital endowments and rates of investment have long been recognised as crucial elements for explaining observed GDP gaps, nevertheless, human capital proxies are rarely significant in growth regressions. In this study some possible solutions to this puzzle are explored. We estimate aggregate returns to education in Italy and Spain, and compare our results with the predictions of competing theoretical frameworks. In general, our empirical analysis identifies a positive role for human capital, and stresses the relevance of theoretical models in which human capital has a fundamental but indirect role in the catching up process. The final part of the thesis proposes a new methodology designed to estimate technology levels and to test whether part of observed convergence is due to technology convergence. The results seem to confirm the existence of technology catch-up among regions

Optimization of net power density in Reverse Electrodialysis

Reverse Electrodialysis (RED) extracts electrical energy from the salinity difference between two solutions using selective ion exchange membranes. In RED, conditions yielding a large net power density (NPD) are generally desired, due to the still large cost of the membranes. NPD depends on a large number of physical and geometric parameters. Some of these, for example the inlet concentrations of concentrate and diluate, can be regarded as “scenario” variables, imposed by external constraints (e.g., availability) or chosen by different criteria than NPD maximization. Others, namely the thicknesses HCONC, HDIL and the velocities UCONC, UDIL in the concentrate and diluate channels, can be regarded as free design parameters and can be chosen so as to maximize NPD. In the present study, a simplified model of a RED stack was coupled with an optimization algorithm in order to determine the conditions of maximum NPD in the space of the variables HCONC, HDIL,UCONC, UDIL for different sets of “scenario” variables. The study shows that an optimal choice of the free design parameters for any given scenario, as opposed to the adoption of standard fixed values for the same parameters, may provide significant improvements in NPD

Finite-momentum Bose-Einstein condensates in shaken 2D square optical lattices

We consider ultracold bosons in a 2D square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. It is therefore necessary to account for higher-order hopping terms, which are renormalized differently by the shaking, and introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates, with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott-insulator and the different superfluid phases, and present the time-of-flight images expected to be observed experimentally. Our results open up new possibilities for the realization of bosonic analogs of the FFLO phase describing inhomogeneous superconductivity.Comment: 7 pages, 7 figure

Experimental investigation of two-side heat transfer in spacer-filled channels

In Membrane Distillation (MD), spacers support the membranes and promote mixing, thus reducing temperature polarization. Their efficient design requires a knowledge of the distribution of the local heat transfer coefficient h and of its dependence on Reynolds number, spacer geometry and flow-spacer relative orientation. In previous work, we applied Thermochromic Liquid Crystals (TLC) and digital image processing to the measurement of h distributions for different spacer configurations; data were used to validate CFD simulations and select turbulence models. For constructive reasons, the test section allowed only one-side heat transfer, while in most MD configurations (e.g. spiral-wound modules) heat transfer occurs from both sides of the feed water channels. Analytical and numerical solutions show that changing from one-side to two-side heat transfer deeply affects h values. This motivated the design and construction of an improved test section in which a hot channel is sandwiched between two cold channels, and twin cameras and lighting equipment allow the simultaneous acquisition of TLC images on both walls. This paper describes this new test section and the experimental technique, discusses measurement uncertainty, and presents preliminary results

Cortical responses to natural speech reflect probabilistic phonotactics

Humans comprehend speech despite the various challenges of real-world environments, such as loud noise and mispronunciation. Our auditory system is robust to these thanks to the integration of the upcoming sensory input with prior knowledge and expectations built on language-specific regularities. One such regularity regards the permissible phoneme sequences, which determine the likelihood that a word belongs to a given language (phonotactic probability; “blick” is more likely to be an English word than “bnick”). Previous research suggested that violations of these rules modulate brain evoked responses such as the N400 and the late positive complex. Yet several fundamental questions remain unresolved, especially regarding the neural encoding and integration strategy of phonotactic information. Here, we used linear modelling approaches to assess the influence of phonotactic probabilities on the brain responses to narrative speech measured with non-invasive EEG. We found that the relationship between continuous speech and EEG responses is best described when the speech descriptor includes phonotactic probabilities. This provides us with a methodology to isolate and measure the brain responses to phonotactics using natural speech at the individual subject-level. Furthermore, such low-frequency signals showed the strongest speech-EEG interactions at latencies of 100-400 ms, supporting a pre-lexical role of phonotactic information

The impact of temporal synchronisation imprecision on TRF analyses

Human sensory perception requires our brains to extract, encode, and process multiple properties of the sensory input. In the context of continuous sensory signals, such as speech and music, the measured electrical neural activity synchronises to properties such as the acoustic envelope, a phenomenon referred to as neural tracking. The ability of measuring neural tracking with non-invasive neurophysiology constitutes an exciting new opportunity for applied research. For example, it enables the objective assessment of cognitive functions in challenging cohorts and environments by using pleasant, everyday tasks, such as watching videos. However, neural tracking has been mostly studied in controlled, laboratory environments guaranteeing precise synchronisation between the neural signal and the corresponding labels (e.g., speech envelope). There exist various challenges that could impact such a temporal precision in, for instance, out-of-lab scenarios, such as technology (e.g., wireless data acquisition), mobility requirements (e.g., clinical scenarios), and the task (e.g., imagery). Aiming to address this type of challenge, we focus on the predominant scenario of continuous sensory experiments involving listening to speech and music. First a temporal response function analysis is presented on two different datasets to assess the impact of trigger imprecision. Second, a proof-of-concept re-alignment methodology is proposed to determine potential issues with the temporal synchronisation. Finally, a use-case study is presented that demonstrates neural tracking measurements in a challenging scenario involving older individuals with neurocognitive decline in care homes. Significance Statement Human cognitive functions can be studied by measuring neural tracking with non-invasive neurophysiology as participants perform pleasant, everyday tasks, such as listening to music. However, while recent work has encouraged the use of this approach in applied research, it remains unclear how robust neural tracking measurements can be when considering the methodological constraints of applied scenarios. This study determines the impact of a key factor for the measurement of neural tracking: the temporal precision of the neural recording. The results provide clear guidelines for future research, indicating what level of imprecision can be tolerated for measuring neural tracking with speech and music listening tasks in both laboratory and applied settings. Furthermore, the study provides a strategy to assess the impact of imprecision in the synchronisation of the neural recording, thus developing new tools for applied neuroscience