Analyzing a Bose polaron across resonant interactions

Recently, two independent experiments reported the observation of long-lived polarons in a Bose-Einstein condensate, providing an excellent setting to study the generic scenario of a mobile impurity interacting with a quantum reservoir. Here, we expand the experimental analysis by disentangling the effects of trap inhomogeneities and the many-body continuum in one of these experiments. This makes it possible to extract the energy of the polaron at a well-defined density as a function of the interaction strength. Comparisons with quantum Monte-Carlo as well as diagrammatic calculations show good agreement, and provide a more detailed picture of the polaron properties at stronger interactions than previously possible. Moreover, we develop a semi-classical theory for the motional dynamics and three-body loss of the polarons, which partly explains a previously unresolved discrepancy between theory and experimental observations for repulsive interactions. Finally, we utilize quantum Monte-Carlo calculations to demonstrate that the findings reported in the two experiments are consistent with each other

Total positivity and accurate computations with Gram matrices of Bernstein bases

In this paper, an accurate method to construct the bidiagonal factorization of Gram (mass) matrices of Bernstein bases of positive and negative degree is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. Numerical examples are included

Total positivity and high relative accuracy for several classes of Hankel matrices

Gramian matrices with respect to inner products defined for Hilbert spaces supported on bounded and unbounded intervals are represented through a bidiagonal factorization. It is proved that the considered matrices are strictly totally positive Hankel matrices and their catalecticant determinants are also calculated. Using the proposed representation, the numerical resolution of linear algebra problems with these matrices can be achieved to high relative accuracy. Numerical experiments are provided, and they illustrate the excellent results obtained when applying the theoretical results

Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases

In this paper we deduce a bidiagonal decomposition of Gram and Wronskian matrices of geometric and Poisson bases. It is also proved that the Gram matrices of both bases are strictly totally positive, that is, all their minors are positive. The mentioned bidiagonal decompositions are used to achieve algebraic computations with high relative accuracy for Gram and Wronskian matrices of these bases. The provided numerical experiments illustrate the accuracy when computing the inverse matrix, the eigenvalues or singular values or the solutions of some linear systems, using the theoretical results

Accurate computations with matrices related to bases {tie¿t}

The total positivity of collocation, Wronskian and Gram matrices corresponding to bases of the form (eλt,teλt,…,tneλt) is analyzed. A bidiagonal decomposition providing the accurate numerical resolution of algebraic linear problems with these matrices is derived. The numerical experimentation confirms the accuracy of the proposed methods

Reconstruction and numerical modelling of the abdominal wall. Application to hernia surgery

Routine hernia repair surgery involves the implant of synthetic mesh. However, this proceduremay give rise to several problems causing considerable patient disability. With the aim ofimproving surgical procedures, the healthy and the herniated human abdomen are simulatedusing finite element (FE) simulations. For that purpose, a reconstruction of the physiologicalgeometry of a human abdomen was created using magnetic resonance images. Besides,following the anatomy of the abdomen, the different muscles and aponeurosis were defined.Furthermore, collagen fibres were included in each muscle layer and their passive anisotropicmechanical contribution was modelled within the framework of hyperelasticity. In the FEsimulation of the abdomen, the constraint imposed by the shoulder is applied and an internalpressure of 23 kPa was applied to the interior abdominal wall to reproduce the abdominal loadwhen standing jumping. After generating a hernia in the front of the abdomen, differentprostheses (Surgipro®, Optilene® and Infinit®), modelled using a membrane model, are placedin the defect to simulate the behaviour of the abdomen after the surgical procedure. In thehealthy abdomen, maximal principal stresses (MPS) and displacements (MD) appear in thefront of the belly. On the other hand, once the hernia is created and the mesh is placed, theMD and MPS are higher than those attained in the healthy abdomen. Thus, just after surgery,surgical repair procedure does not fully restore normal physiological conditions and the risk ofhernia recurrence by the suture is high due to the stress concentration

Segal-Bargmann-Fock modules of monogenic functions

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.Comment: 11 page