Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench

We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions, and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting (and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However, due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.Comment: 15 pages, 11 figure

Non-equilibrium quantum dynamics : interplay of disorder, interactions and confinement

The study of collective behaviour in many-body systems often explores fundamentally new ideas absent from the mere constituents of such a system. A paradigmatic model for these studies is the spin-1/2 XXZ chain and its fermionic equivalent. This thesis can be broadly divided into the study of two fundamental aspects of this model. Firstly, we discuss localisation phenomena in one dimensional lattices as often experimentally realised in cold atom systems. Secondly, we investigate how disorder and symmetry influence heat transport in spin chains. More specifically, in the first part we consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of a strong optical lattice, a harmonic trap, and uncorrelated on-site disorder. We investigate a global inhomogeneous quantum quench and present numerical and analytical results for static and dynamical properties. We show that the approach to the non-thermal equilibrium state is extremely slow and that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localisation. We also consider the above system in a strong non-uniform electric field. In the non-interacting case, due to Wannier-Stark localisation, the single-particle wave functions are exponentially localised without quenched disorder. We show that this system remains localised in the presence of nearest-neighbour interactions and exhibits physics analogous to models of conventional many-body localisation. The second part explores the hydrodynamics of the disordered XYZ spin chain. Using time-evolving block decimation on open chains of up to 400 spins attached to thermal baths, we probe the energy transport of this system. Our principal findings are as follows. For weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Then, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive.Funded by CM-CDT and EPSRC (UK) under grants EP/G03673X/1 and EP/L015110/1

Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS). Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. Data is acquired with a 3D Radial Phase Encoding (RPE) trajectory and an iterative reweighting scheme is used during image reconstruction to ensure fast convergence and high image quality. In our in-vivo cardiac MRI experiments we show that the proposed method 3DShearCS has lower relative errors and higher structural similarity compared to the other reconstruction techniques especially for high undersampling factors, i.e. short scan times. In this paper, we further show that 3DShearCS provides improved depiction of cardiac anatomy (measured by assessing the sharpness of coronary arteries) and two clinical experts qualitatively analyzed the image quality

A spatially resolved in-situ calibration applied to infrared thermography

When using thermography at elevated ambient temperature levels to determine the surface temperature of test specimen, radiation reflected on the test surfaces can lead to a large measurement error. Calibration methods accounting for this amount of radiation are available in the open literature. Those methods, however, only account for a scalar calibration parameter. With new, complex test rigs and inhomogeneous reflected radiation distribution, the need for a spatially resolved calibration arises. Therefore, this paper presents a new correction method accounting for a spatially varying reflected radiation. By computing a geometrical raytracing, a spatially resolved correction factor is determined. An extended calibration technique based on an in situ approach is proposed, allowing a local correction of reflected radiation. This method is applied to a test case with defined boundary conditions. The results are compared to a well-known in situ calibration method. A major improvement in measurement accuracy is achieved: the error in calibrated temperature can be reduced from over 10% to well below 2.5%. This reduction in error is especially prominent when the test surfaces are colder than the hot ambient, which is the case in many cooling applications, e.g. in gas turbine cooling researc

Rhenium(V) complexes with selenolato‐ and tellurolato‐substituted Schiff bases – Released PPh3 as a facile reductant

The salicylidene Schiff bases of bis(2‐aminophenyl)diselenide and ‐ditelluride react with [ReOCl3(PPh3)2] or the arylimidorhenium(V) compounds [Re(NPhR)Cl3(PPh3)2] (R = H, F, CF3) with formation of rhenium(V) complexes with tridentate {O,N,Se/Te} chalcogenolato ligands. The ligands adopt a facial coordination mode with the oxygen donors trans to the multiply bonded O2– or NPhR2– ligands. The reduction of the dichalcogenides and the formation of the chalcogenolato ligands occurs in situ by released PPh3 ligands. The absence of additional reducing agents provides good yields of products with rhenium in the high formal oxidation state “+5”. A mechanism for the dichalcogenide reduction is proposed on the basis of the experimental results. In accordance with the proposed mechanism, best yields are obtained with a strict exclusion of oxygen, but in the presence of water

Preparativne modifikacije askomicina. V. Dobivanje novih derivata pomoću zamjene cikloheksilvinilidenske podjedinice

Starting from the easily accessible 24-O-tert-butyldimethylsilyl-22(R)-dihydro-28-oxoascomycin, methodologies that allow replacement of the cyclohexylvinylidene moiety of ascomycin by various other substituents are described. In addition, a so far unknown reactivity of the masked tricarbonyl moiety of ascomycin towards a stabilized Wittig reagent is reported.Opisani su postupci koji počinju s lako pristupačnim 25-O-tert-butildimetilsilil-22(R)-dihidro-28-oksoaskomicinom i omogućuju zamjenu askomicinske cikloheksilvinilidenske podjedinice različitim substituentima

The Unique Ambiphilicity of Tellurium in the [MesitylTe(I)(I2)(I3)]− Anion

A first example of an aryltellurium(II) compound with three different bonding modes to iodine featuring covalent and non-covalent bonds such as two orthogonal, ambiphilic σ-hole interactions is introduced: [MesTe(I)(I2)(I3)]−. It is a member of a series of mesityltellurenyl anions, which are formed during reactions of (MesTe)2 with ZnI2, phenanthroline (phen) and iodine. [Zn(phen)3][MesTe(I)2] (1), [Zn(phen)3][{MesTe(I)-(I)…Te(I)Mes}{MesTeI2}] (2) and [Zn(phen)3][MesTe(I)(I2)(I3)][MesTeI2] (3) are isolated depending on the amount of iodine used. The products contain tellurium atoms bonded to a variety of iodine species (I−, μ2-I−, I2 and I3−) and are, thus, perfectly suitable to explore the amphiphilic behavior of tellurium(II) and its relevance for the formation of non-covalent bonds, where tellurium acts as both donor and acceptor simultaneously. The character of chalcogen and halogen bonds are evaluated by the combination of crystallographic data and computational methods