We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a chargedensity wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)]. arXiv:1808.01250v2 [cond-mat.dis-nn]
PACS 74.62.En -Effects of disorder PACS 64.60.an -Finite-size systems (General studies of phase transitions) PACS 72.15.Rn -Localization effects (Anderson or weak localization)Abstract -We present a detailed analysis of the length-and timescales needed to approach the critical region of MBL from the delocalised phase, studying both eigenstates and the time evolution of an initial state. For the eigenstates we show that in the delocalised region there is a single length, which is a function of disorder strength, controlling the finite-size flow. Small systems look localised, and only for larger systems do resonances develop which restore ergodicity in the form of the eigenstate thermalisation hypothesis. For the transport properties, we study the time necessary to transport a single spin across a domain wall, showing how this grows quickly with increasing disorder, and compare it with the Heisenberg time. For a sufficiently large system the Heisenberg time is always larger than the transport time, but for a smaller system this is not necessarily the case. We conclude that the properties of the MBL transition cannot be explored using the system sizes or times available to current numerical and experimental studies.
Background: White matter hyperintensities of presumed vascular origin (WMH) are a common finding in elderly people and a growing social malady in the aging western societies. As a manifestation of cerebral small vessel disease, WMH are considered to be a vascular contributor to various sequelae such as cognitive decline, dementia, depression, stroke as well as gait and balance problems. While pathophysiology and therapeutical options remain unclear, large-scale studies have improved the understanding of WMH, particularly by quantitative assessment of WMH. In this review, we aimed to provide an overview of the characteristics, research subjects and segmentation techniques of these studies. Methods: We performed a systematic review according to the PRISMA statement. One thousand one hundred and ninety-six potentially relevant articles were identified via PubMed search. Six further articles classified as relevant were added manually. After applying a catalog of exclusion criteria, remaining articles were read full-text and the following information was extracted into a standardized form: year of publication, sample size, mean age of subjects in the study, the cohort included, and segmentation details like the definition of WMH, the segmentation method, reference to methods papers as well as validation measurements. Results: Our search resulted in the inclusion and full-text review of 137 articles. One hundred and thirty-four of them belonged to 37 prospective cohort studies. Median sample size was 1,030 with no increase over the covered years. Eighty studies investigated in the association of WMH and risk factors. Most of them focussed on arterial hypertension, diabetes mellitus type II and Apo E genotype and inflammatory markers. Sixty-three studies analyzed the association of WMH and secondary conditions like cognitive decline, mood disorder and brain atrophy. Studies applied various methods based on manual (3), semi-automated (57), and automated segmentation techniques (75). Only 18% of the articles referred to an explicit definition of WMH. Discussion: The review yielded a large number of studies engaged in WMH research. A remarkable variety of segmentation techniques was applied, and only a minority referred to a clear definition of WMH. Most addressed topics were risk factors and secondary clinical conditions. In conclusion, WMH research is a vivid field with a need for further standardization regarding definitions and used methods.
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