Algebraic equivalence between certain models for superfluid--insulator transition

Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg model, the Quantum Phase Model, and the Bose Hubbard Model is established as the contractions of the algebra $u(2)$ underlying the dynamics of the $XXZ$ Heisenberg model.Comment: 5 pages, revte

Optimal correlations in many-body quantum systems

Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics. To this aim we adopt the information-theory view of correlations, and study the amount of correlations after certain classes of Positive-Operator-Valued Measurements are locally performed. As many-body system we consider a one-dimensional array of interacting two-level systems (a spin chain) at zero temperature, where quantum effects are most pronounced. We demonstrate how the optimal strategy to extract the correlations depends on the quantum phase through a subtle interplay between local interactions and coherence.Comment: 5 pages, 5 figures + supplementary material. To be published in PR

Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.

Dynamics of Global Entanglement under Decoherence

We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important class of multi-partite entangled states, the Greenberger-Horne-Zeilinger and the W state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the W state, consistent with previous studies.Comment: 5 pages and 5 figure

Deep reinforcement learning for active control of a three-dimensional bluff body wake

The application of deep reinforcement learning (DRL) to train an agent capable of learning control laws for pulsed jets to manipulate the wake of a bluff body is presented and discussed. The work has been performed experimentally at a value of the Reynolds number Re similar to 10(5) adopting a single-step approach for the training of the agent. Two main aspects are targeted: first, the dimension of the state, allowing us to draw conclusions on its effect on the training of the neural network; second, the capability of the agent to learn optimal strategies aimed at maximizing more complex tasks identified with the reward. The agent is trained to learn strategies that minimize drag only or minimize drag while maximizing the power budget of the fluidic system. The results show that independently on the definition of the reward, the DRL learns forcing conditions that yield values of drag reduction that are as large as 10% when the reward is based on the drag minimization only. On the other hand, when also the power budget is accounted for, the agent learns forcing configurations that yield lower drag reduction (5%) but characterized by large values of the efficiency. A comparison between the natural and the forced conditions is carried out in terms of the pressure distribution across the model's base. The different structure of the wake that is obtained depending on the training of the agent suggests that the possible forcing configuration yielding similar values of the reward is local minima for the problem. This represents, to the authors' knowledge, the first application of a single-step DRL in an experimental framework at large values of the Reynolds number to control the wake of a three-dimensional bluff body. Published under an exclusive license by AIP Publishing

Wall bounded flows manipulation using sinusoidal riblets

We experimentally investigate the effects of microgrooves on the development of a zero pressure gradient turbulent boundary layer. Starting from the well-known streamwise aligned riblets, we look at the effect of wavy riblets, characterized by a sinusoidal pattern in the mean flow direction. We perform hot wire experiments as well as particle image velocimetry to get some insights on the effect of the sinusoidal shape on the near wall organisation of the boundary layer. The statistical analysis clearly shows that the wavy pattern has a strong influence on the near wall structure of the boundary layer. The statistical analysis performed using the VITA technique reveals that the coherent structures that characterize the turbulent boundary layer are attenuated by the geometry manipulation. Furthermore, the POD reconstructed velocity fields, measured with PIV, reveal that the manipulation tampers with the momentum exchange occurring between the near wall and the outer region of the boundary layer, hence suggesting a modified turbulence production cycle

Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of refs. modifie

Adiabatic dynamics in open quantum critical many-body systems

The purpose of this work is to understand the effect of an external environment on the adiabatic dynamics of a quantum critical system. By means of scaling arguments we derive a general expression for the density of excitations produced in the quench as a function of its velocity and of the temperature of the bath. We corroborate the scaling analysis by explicitly solving the case of a one-dimensional quantum Ising model coupled to an Ohmic bath.Comment: 4 pages, 4 figures; revised version to be published in Phys. Rev. Let

Towards Subject and Diagnostic Identifiability in the Alzheimer’s Disease Spectrum Based on Functional Connectomes

Alzheimer’s disease (AD) is the only major cause of mortality in the world without an effective disease modifying treatment. Evidence supporting the so called “disconnection hypothesis” suggests that functional connectivity biomarkers may have clinical potential for early detection of AD. However, known issues with low test-retest reliability and signal to noise in functional connectivity may prevent accuracy and subsequent predictive capacity. We validate the utility of a novel principal component based diagnostic identifiability framework to increase separation in functional connectivity across the Alzheimer’s spectrum by identifying and reconstructing FC using only AD sensitive components or connectivity modes. We show that this framework (1) increases test-retest correspondence and (2) allows for better separation, in functional connectivity, of diagnostic groups both at the whole brain and individual resting state network level. Finally, we evaluate a posteriori the association between connectivity mode weights with longitudinal neurocognitive outcomes