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. 10, 198 (2014)], realizing a gas with tunable SU (κ) 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 κ components of the gas and the Young tableaux for the SN permutation symmetry group identifying the magnetic structure of the groundstate. 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, we study the Tan's contact behaviour at large temperatures and in the limit of infinite interactions and we show that it 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. 10, 198 (2014)].

We consider a mixture of one-dimensional strongly interacting Fermi gases with up to six components, subjected to a longitudinal harmonic confinement. In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture. We show that an imbalanced mixture under harmonic confinement displays partial spatial separation among the components, with a structure which depends on the relative population of the various components. Furthermore, we provide a symmetry characterization of the ground and excited states of the mixture introducing and evaluating a suitable operator, namely the conjugacy class sum. We show that, even under external confinement, the gas has a definite symmetry which corresponds to the most symmetric one compatible with the imbalance among the components. This generalizes the predictions of the Lieb-Mattis theorem for a fermionic mixture with more than two components.

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.

One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to quantum simulation and quantum computation due to their computational complexity. In this article, we exploit spectral graph theory to completely characterize the symmetry properties of one-dimensional fermionic mixtures in the strong interaction limit. We also develop a powerful method to obtain the so-called Tan contacts associated with certain symmetry classes. In particular, compared to brute-force diagonalization that is already virtually impossible for a moderate number of fermions, our analysis enables us to make unprecedented efficient predictions about the energy gap of complex spin mixtures. Our theoretical results are not only of direct experimental interest but also provide important guidance for the design of adiabatic control protocols in strongly correlated fermion mixtures.

We compute the Tan's contact of a weakly interacting Bose gas at zero temperature in a cigarshaped configuration. Using an effective one-dimensional Gross-Pitaevskii equation and Bogoliubov theory, we derive an analytical formula that interpolates between the three-dimensional and the one-dimensional mean-field regimes. In the strictly one-dimensional limit, we compare our results with Lieb-Liniger theory. Our study can be a guide for actual experiments interested in the study of Tan's contact in the dimensional crossover.

We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental importance in both classical and quantum physics, and to completely characterize their algebraic structure. Notably, we prove that the spectral gap can be obtained in polynomial computational time, which has strong implications in the context of adiabatic quantum computing with quantum spin chains. This quantity also characterizes the rate to stationarity of some important classical random processes such as interchange and exclusion processes. Reciprocally, we use results derived from the celebrated Bethe ansatz to obtain mathematical results about these graphs in the unweighted case. We also discuss extensions of this unifying framework to other systems, such as asymmetric exclusion processes-a paradigmatic model in nonequilibrium physics-or the more exotic non-Hermitian quantum systems.

Background: Coronary artery disease distribution along the vessel is a main determinant of FFR improvement after PCI. Identifying focal from diffuse disease from visual inspections of coronary angiogram (CA) and FFR pullback (FFR-PB) are operator-dependent. Computer science may standardize interpretations of such curves.Methods: A virtual stenting algorithm (VSA) was developed to perform an automated FFR-PB curve analysis. A survey analysis of the evaluations of 39 vessels with intermediate disease on CA and a distal FFR <0.8, rated by 5 interventional cardiologists, was performed. Vessel disease distribution and PCI strategy were successively rated based on CA and distal FFR (CA); CA and FFR-PB curve (CA/FFR-PB); and CA and VSA (CA/VSA). Inter-rater reliability was assessed using Fleiss kappa and an agreement analysis of CA/VSA rating with both algorithmic and human evaluation (operator) was performed. We hypothesize that VSA would increase rater agreement in interpretation of epicardial disease distribution and subsequent evaluation of PCI eligibility.Results: Inter-rater reliability in vessel disease assessment by CA, CA/FFR-PB, and CA/VSA were respectively, 0.32 (95% CI: 0.17–0.47), 0.38 (95% CI: 0.23–0.53), and 0.4 (95% CI: 0.25–0.55). The raters' overall agreement in vessel disease distribution and PCI eligibility was higher with the VSA than with the operator (respectively, 67 vs. 42%, and 80 vs. 70%, both p < 0.05). Compared to CA/FFR-PB, CA/VSA induced more reclassification toward a focal disease (92 vs. 56.2%, p < 0.01) with a trend toward more reclassification as eligible for PCI (70.6 vs. 33%, p = 0.06). Change in PCI strategy did not differ between CA/FFR-PB and CA/VSA (23.6 vs. 28.5%, p = 0.38).Conclusions: VSA is a new program to facilitate and standardize the FFR pullback curves analysis. When expert reviewers integrate VSA data, their assessments are less variable which might help to standardize PCI eligibility and strategy evaluations.Clinical Trial Registration:https://www.clinicaltrials.gov/ct2/show/NCT03824600.

Background Guidelines recommend hemodynamic/functional assessment to guide treatment decision making in stable coronary artery disease. A Fractional flow reserve (FFR) motorized pullback allows a reproducible assessment of the distribution of pressure drop generated by coronary artery disease along the vessel and may provide more relevant hemodynamic information than a single distal FFR value. Purpose We aimed to assess the agreement between the revascularization strategy guided by coronary angiogram and a single distal FFR value interpretation (standard of care, SOC), and a treatment recommendation by a fully automated analysis of pullback FFR curves by an in-house developed computer-based algorithm (CBA). Methods Pullback FFR curves were recorded under continuous intra-venous adenosine in patients with intermediate coronary stenosis by using a motorized device working at a speed of 1 mm/s (Volcano R 100) set to grip a pressure wire. A proprietary algorithm (JD, Mathematica v.11) was applied to: 1) assess the distal FFR on the last 5 mm of the curves, 2) discriminate a stepwise from a progressive decrease of FFR, 3) propose a treatment strategy between optimal medical treatment (OMT), PCI (including the number, length(s) and position(s) of the stent) or CABG, 4) evaluate the post PCI expected change in FFR. A concordance analysis between effective and CBA recommended treatment was performed. Only curves with distal FFR ≤0.85 were included into the analysis. If post PCI FFR was recorded, CBA predicted and measured post PCI FFR were compared. Results 50 vessels from 43 patients (75% LAD, 10% Cx, 15% RCA) with a distal FFR of 0.78±0.08 were assessed. A revascularization was performed in 29 vessels (24 PCI, 5 CABG). Post PCI FFR pullback was recorded in 11 vessels. Compared to SOC, a similar proportion of vessels was referred for revascularization by CBA (56 vs. 58% respectively, Chi2 0.041, p NS). Agreement between SOC and CBA, regarding the need of a revascularization, was observed in 76% of cases. Observed Cohen's Kappa coefficient for OMT, PCI or CABG revascularization strategy was 0.48 (CI 95%: 0.26–0.7). A mismatch between SOC and CBA strategy was observed in 30% (n=15) of vessels. A post hoc examination of FFR pullback curves showed that CBA decision might have been appropriate in 80% of these mismatches. Reclassification of treatment strategy by CBA was related to misinterpretation of one single FFR value (40%, n=6), incorrect detection of significant stepwise decrease in FFR (33%, n=5) and incorrect detection of progressive decrease in FFR (7%, n=1) by SOC approach. A mean bias of 0.01 (CI 95% −0.05–0.07) was observed between CBA predicted and measured post PCI FFR. Conclusion CBA recommended treatment differs from SOC treatment in almost 1/3 of vessels. CBA of FFR pullback curves offers new opportunity to guide myocardial revascularization stategy and warrants further prospective evaluation.