Benchmarking a Novel Efficient Numerical Method for Localized 1D Fermi-Hubbard Systems on a Quantum Simulator

Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in principle able to simulate quantum dynamics well outside the domain of classical computers, they are noisy and limited in the variability of the initial state of the dynamics and the observables that can be measured. Despite these limitations, here we show that such a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We develop an efficient numerical technique that facilitates classical simulations in regimes not accessible to exact calculations or other established numerical techniques. The method is based on approximations that are well suited to describe localized one-dimensional Fermi-Hubbard systems. Since this new method does not have an error estimate and the approximations do not hold in general, we use a neutral-atom Fermi-Hubbard quantum simulator with $L_{\text{exp}}\simeq290$ lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to $700$ tunnelling times. We then use these approximations in order to derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system we consider is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.Comment: 24 pages, 10 figure

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.Comment: accepted in Nature Communication

Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model

We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly-interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench

Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model.

We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench

Sexual experience affects reproductive behavior and preoptic androgen receptors in male mice

Reproductive behavior in male rodents is made up of anticipatory and consummatory elements which are regulated in the brain by sensory systems, reward circuits and hormone signaling. Gonadal steroids play a key role in the regulation of male sexual behavior via steroid receptors in the hypothalamus and preoptic area. Typical patterns of male reproductive behavior have been characterized, however these are not fixed but are modulated by adult experience. We assessed the effects of repeated sexual experience on male reproductive behavior of C57BL/6 mice; including measures of olfactory investigation of females, mounting, intromission and ejaculation. The effects of sexual experience on the number of cells expressing either androgen receptor (AR) or estrogen receptor alpha (ERα) in the primary brain nuclei regulating male sexual behavior was also measured. Sexually experienced male mice engaged in less sniffing of females before initiating sexual behavior and exhibited shorter latencies to mount and intromit, increased frequency of intromission, and increased duration of intromission relative to mounting. No changes in numbers of ERα-positive cells were observed, however sexually experienced males had increased numbers of AR-positive cells in the medial preoptic area (MPOA); the primary regulatory nucleus for male sexual behavior. These results indicate that sexual experience results in a qualitative change in male reproductive behavior in mice that is associated with increased testosterone sensitivity in the MPOA and that this nucleus may play a key integrative role in mediating the effects of sexual experience on male behavior

Business analytics in industry 4.0: a systematic review

Recently, the term “Industry 4.0” has emerged to characterize several Information Technology and Communication (ICT) adoptions in production processes (e.g., Internet-of-Things, implementation of digital production support information technologies). Business Analytics is often used within the Industry 4.0, thus incorporating its data intelligence (e.g., statistical analysis, predictive modelling, optimization) expert system component. In this paper, we perform a Systematic Literature Review (SLR) on the usage of Business Analytics within the Industry 4.0 concept, covering a selection of 169 papers obtained from six major scientific publication sources from 2010 to March 2020. The selected papers were first classified in three major types, namely, Practical Application, Reviews and Framework Proposal. Then, we analysed with more detail the practical application studies which were further divided into three main categories of the Gartner analytical maturity model, Descriptive Analytics, Predictive Analytics and Prescriptive Analytics. In particular, we characterized the distinct analytics studies in terms of the industry application and data context used, impact (in terms of their Technology Readiness Level) and selected data modelling method. Our SLR analysis provides a mapping of how data-based Industry 4.0 expert systems are currently used, disclosing also research gaps and future research opportunities.The work of P. Cortez was supported by FCT - Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020. We would like to thank to the three anonymous reviewers for their helpful suggestions

Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model.

We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench