Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.Comment: 5 pages + supplemental material, 6 figure

Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations

We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb-Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan's contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.Comment: 19 pages, 6 figure

High-momentum tails as magnetic structure probes for strongly-correlated SU(κ)SU(\kappa) fermionic mixtures in one-dimensional traps

A universal $k^{-4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. {\bf 10}, 198 (2014)], realizing a gas with tunable $SU(\kappa)$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\kappa$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground-state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach in the limit of infinite interactions, we show that the contact increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref.~[Nat. Phys. {\bf 10}, 198 (2014)].Comment: 13 pages, 6 figure

Integrating Topological Proofs with Model Checking to Instrument Iterative Design

System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each refinement or revision step. To achieve practical adoption, formal verification must accommodate continuous verification efficiently and effectively. Model checking provides developers with information useful to improve their models only when a property is not satisfied, i.e., when a counterexample is returned. However, it is desirable to have some useful information also when a property is instead satisfied. To address this problem we propose TOrPEDO, an approach that supports verification in two complementary forms: model checking and proofs. While model checking is typically used to pinpoint model behaviors that violate requirements, proofs can instead explain why requirements are satisfied. In our work, we introduce a specific notion of proof, called Topological Proof. A topological proof produces a slice of the original model that justifies the property satisfaction. Because models can be incomplete, TOrPEDO supports reasoning on requirements satisfaction, violation, and possible satisfaction (in the case where satisfaction depends on unknown parts of the model). Evaluation is performed by checking how topological proofs support software development on 12 modeling scenarios and 15 different properties obtained from 3 examples from literature. Results show that: (i) topological proofs are ≈60% smaller than the original models; (ii) after a revision, in ≈78% of cases, the property can be re-verified by relying on a simple syntactic check

Preliminary Characterization of a Functional Jam from Red Chicory By-Product

Background: The by-products of red chicory leaves are a valuable source of bioactive compounds that can be exploited in the development of functional foods. Objective: This work aimed to combine healthy properties of red chicory by-products with other ingredients in the formulation of a functional jam, which is easy and safe to swallow, especially for people suffering from dysphagia. Methods: The physicochemical parameters, as well as the total polyphenols content (TPC), was assessed in the obtained product. Results: The TPC (549.44 mg GAE/100 g) was higher than the values reported in other jams, and it remained stable along with the colour during six weeks of storage. Within the carbohydrates, 0.4% of the prebiotic fibre inulin has been detected, suggestingthat this jam formulation is a promising delivery system of phenols and fibre. From the sensorial point of view, the functional jam obtained an overall good acceptability judgment.The bitterness of the red chicory is persistent, which helps people with dysphagia swallow more easily. Conclusion: The functional jam, based on chicory by-products, could be a good source of bioactive compounds, which are helpful even in the disabled subjects’ diet

Tax evasion, behavioral microsimulation models and flat-rate tax reforms. Analysis for Italy

It is sometimes argued that a flat-rate tax reform can reduce tax noncompliance. The argument is, however, inconsistent with the so-called Yitzhaki’s puzzle of the classical expected utility (EU) model. The latter predicts an increase, rather than a reduction, in tax evasion following a cut in the tax rates resulting from a flat-rate reform. We study the impact of a flat-rate tax in a microsimulation tax-benefit model of Italy which allows us to analyse various hypotheses of tax evasion behavior. In addition to the EU model, we analyse expected utility with rank dependent probabilities (EURDP) and the model of reference dependent (RD) preference, the most favourable to overturn Yitzhaki’s puzzle. Our simulations show that a flat-rate tax would barely reduce overall evasion in Italy in all models considered. Redistributive effects are in all cases large