Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N)(N) Hubbard models

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.Comment: 11 pages, 3 figures. Fixed sign error in eqs. (14,16,17,18). This error had no effect on any of the numerical results or conclusion

Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice

We investigate the properties of a Tonks-Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.Comment: 24 pages, 12 figure

Quenched and Driven Dynamics of One-Dimensional Quantum Systems

This thesis focuses on quenched and driven dynamics in interacting quantum systems that cannot be treated with mean-field approximations. The majority of the work is related to the unitary dynamics induced in one-dimensional systems due to a sudden change in a physical parameter (a quench). Such systems can be realized in cold atomic gases where the degree of experimental control also enables sudden changes in the physical parameters. The dynamics associated with underlying many-body phases and phase transitions for strongly interacting particles in a one-dimensional optical lattice and the relation between work statistics and scrambling dynamics for interacting particles in a harmonic trap are investigated. A more accurate exact diagonalization method useful for calculating the quench dynamics of small finitely interacting systems is also presented. Finally an investigation of an optomechanical system with a new type of nonlinear position-modulated Kerr coupling is presented. This is treated as an open quantum system which reaches a steady-state due to the interplay of driving and dissipation.Okinawa Institute of Science and Technology Graduate Universit

Quantum chaos in interacting Bose-Bose mixtures

The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an advanced exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.Comment: 25 pages, 8 figure

Frictional contact of soft polymeric shells

The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact behavior when a soft elastic shell comes into contact with a flat surface. The deviation from Hertzian contact first arises from bending within the contact area, followed by the second transition induced by buckling, resulting in a notable decrease in the contact area despite increased contact force. Friction delays both transitions and introduces hysteresis during unloading. However, a high amount of friction suppresses both buckling and dissipation. Different contact regimes are discussed in terms of rolling and sliding mechanisms, providing insights for tailoring contact behaviors in soft shells

L-SeqSleepNet: Whole-cycle Long Sequence Modelling for Automatic Sleep Staging

Human sleep is cyclical with a period of approximately 90 minutes, implying long temporal dependency in the sleep data. Yet, exploring this long-term dependency when developing sleep staging models has remained untouched. In this work, we show that while encoding the logic of a whole sleep cycle is crucial to improve sleep staging performance, the sequential modelling approach in existing state-of-the-art deep learning models are inefficient for that purpose. We thus introduce a method for efficient long sequence modelling and propose a new deep learning model, L-SeqSleepNet, which takes into account whole-cycle sleep information for sleep staging. Evaluating L-SeqSleepNet on four distinct databases of various sizes, we demonstrate state-of-the-art performance obtained by the model over three different EEG setups, including scalp EEG in conventional Polysomnography (PSG), in-ear EEG, and around-the-ear EEG (cEEGrid), even with a single EEG channel input. Our analyses also show that L-SeqSleepNet is able to alleviate the predominance of N2 sleep (the major class in terms of classification) to bring down errors in other sleep stages. Moreover the network becomes much more robust, meaning that for all subjects where the baseline method had exceptionally poor performance, their performance are improved significantly. Finally, the computation time only grows at a sub-linear rate when the sequence length increases.Comment: 9 pages, 4 figures, updated affiliation

SUDS, LID, BMPs, WSUD and more - The evolution and application of terminology surrounding urban drainage

Open Access articleThe management of urban stormwater has become increasingly complex over recent decades. Consequently, terminology describing the principles and practices of urban drainage has become increasingly diverse, increasing the potential for confusion and miscommunication. This paper documents the history, scope, application and underlying principles of terms used in urban drainage and provides recommendations for clear communication of these principles. Terminology evolves locally and thus has an important role in establishing awareness and credibility of new approaches and contains nuanced understandings of the principles that are applied locally to address specific problems. Despite the understandable desire to have a ‘uniform set of terminology’, such a concept is flawed, ignoring the fact that terms reflect locally shared understanding. The local development of terminology thus has an important role in advancing the profession, but authors should facilitate communication between disciplines and between regions of the world, by being explicit and accurate in their application

A dual-tag microarray platform for high-performance nucleic acid and protein analyses

DNA microarrays serve to monitor a wide range of molecular events, but emerging applications like measurements of weakly expressed genes or of proteins and their interaction patterns will require enhanced performance to improve specificity of detection and dynamic range. To further extend the utility of DNA microarray-based approaches we present a high-performance tag microarray procedure that enables probe-based analysis of as little as 100 target cDNA molecules, and with a linear dynamic range close to 105. Furthermore, the protocol radically decreases the risk of cross-hybridization on microarrays compared to current approaches, and it also allows for quantification by single-molecule analysis and real-time on-chip monitoring of rolling-circle amplification. We provide proof of concept for microarray-based measurement of both mRNA molecules and of proteins, converted to tag DNA sequences by padlock and proximity probe ligation, respectively

A genetically modified minipig model for Alzheimer's disease with SORL1 haploinsufficiency

The established causal genes in Alzheimer’s disease (AD), APP, PSEN1, and PSEN2, are functionally characterized using biomarkers, capturing an in vivo profile reflecting the disease’s initial preclinical phase. Mutations in SORL1, encoding the endosome recycling receptor SORLA, are found in 2%–3% of individuals with early-onset AD, and SORL1 haploinsufficiency appears to be causal for AD. To test whether SORL1 can function as an AD causal gene, we use CRISPR-Cas9-based gene editing to develop a model of SORL1 haploinsufficiency in Göttingen minipigs, taking advantage of porcine models for biomarker investigations. SORL1 haploinsufficiency in young adult minipigs is found to phenocopy the preclinical in vivo profile of AD observed with APP, PSEN1, and PSEN2, resulting in elevated levels of β-amyloid (Aβ) and tau preceding amyloid plaque formation and neurodegeneration, as observed in humans. Our study provides functional support for the theory that SORL1 haploinsufficiency leads to endosome cytopathology with biofluid hallmarks of autosomal dominant AD