Behavior of quantum entropies in polaronic systems

Quantum entropies and state distances are analyzed in polaronic systems with short range (Holstein model) and long range (Fr$\ddot{o}$hlich model) electron-phonon coupling. These quantities are extracted by a variational wave function which describes very accurately polaron systems with arbitrary size in all the relevant parameter regimes. With the use of quantum information tools, the crossover region from weak to strong coupling regime can be characterized with high precision. Then, the linear entropy is found to be very sensitive to the range of the electron-phonon coupling and the adiabatic ratio. Finally, the entanglement entropy is studied as a function of the system size pointing out that it not bounded, but scales as the logarithm of the size either for weak electron-phonon coupling or for short range interaction. This behavior is ascribed to the peculiar coupling induced by the single electron itinerant dynamics on the phonon subsystem.Comment: 4 figures, to be published in Phys. Rev.

Preface

The aim of this volume is to advance the understanding of linear spaces of symmetric matrices. These seemingly simple objects play many different roles across several fields of mathematics. For instance, in algebraic statistics these spaces appear as linear Gaussian covariance or concentration models, while in enumerative algebraic geometry they classically represent spaces of smooth quadrics satisfying certain tangency conditions. In semidefinite programming, linear spaces of symmetric matrices define the spectrahedra on which optimization problems are considered, and in nonlinear algebra they encode partially symmetric tensors. It is often the case that one of the above-mentioned fields inspires or pro- vides tools for the advancement of the others. In the articles that follow, the reader will find several examples where this has happened through the common link of linear spaces of symmetric matrices. This volume is the culmination of a collaboration project with the same name, which began at MPI Leipzig in June 2020. Over the course of several months, about 40 researchers gathered on-line to work on the ideas and projects that eventually became the articles of this special issue. We are grateful to Bernd Sturmfels for initiating the project and for being its driving force, in particular for presenting the list of open problems that served as a starting point for the working groups that formed. Many of his conjectures became theorems in this volume. We thank Biagio Ricceri and the editorial team of Le Matematiche for co- ordinating the publication of this volume. Finally, thanks to all participants for their contributions to the talks, discussions, and articles around the project

Rashba effect induced localization in quantum networks

We study a quantum network extending in one-dimension (chain of square loops connected at one vertex) made up of quantum wires with Rashba spin-orbit coupling. We show that the Rashba effect may give rise to an electron localization phenomenon similar to the one induced by magnetic field. This localization effect can be attributed to the spin precession due to the Rashba effect. We present results both for the spectral properties of the infinite chain, and for linear transport through a finite-size chain connected to leads. Furthermore, we study the effect of disorder on the transport properties of this network.Comment: To appear in Phys. Rev. Let

Rashba quantum wire: exact solution and ballistic transport

The effect of Rashba spin-orbit interaction in quantum wires with hard-wall boundaries is discussed. The exact wave function and eigenvalue equation are worked out pointing out the mixing between the spin and spatial parts. The spectral properties are also studied within the perturbation theory with respect to the strength of the spin-orbit interaction and diagonalization procedure. A comparison is done with the results of a simple model, the two-band model, that takes account only of the first two sub-bands of the wire. Finally, the transport properties within the ballistic regime are analytically calculated for the two-band model and through a tight-binding Green function for the entire system. Single and double interfaces separating regions with different strengths of spin-orbit interaction are analyzed injecting carriers into the first and the second sub-band. It is shown that in the case of a single interface the spin polarization in the Rashba region is different from zero, and in the case of two interfaces the spin polarization shows oscillations due to spin selective bound states

Rashba effect in quantum networks

We present a formalism to study quantum networks made up by single-channel quantum wires in the presence of Rashba spin-orbit coupling and magnetic field. In particular, linear transport through one-dimensional and two-dimensional finite-size networks is studied by means of the scattering formalism. In some particular quantum networks, the action of the magnetic field or of the Rashba spin-orbit coupling induces localization of the electron wave function. This phenomenon, which relies on both the quantum-mechanical interference and the geometry of the network, is manifested through the suppression of the conductance for specific values of the spin-orbit-coupling strength or of the magnetic field. Furthermore, the interplay of the Aharonov-Bohm phases and of the non-Abelian phases introduced by spin-orbit coupling, is discussed in a number of cases.Comment: 8 pages and 6 figure

Radiogenomics in clear cell renal cell carcinoma: correlations between advanced CT imaging (texture analysis) and microRNAs expression

Purpose: A relevant challenge for the improvement of clear cell renal cell carcinoma management could derive from the identification of novel molecular biomarkers that could greatly improve the diagnosis, prognosis, and treatment choice of these neoplasms. In this study, we investigate whether quantitative parameters obtained from computed tomography texture analysis may correlate with the expression of selected oncogenic microRNAs. Methods: In a retrospective single-center study, multiphasic computed tomography examination (with arterial, portal, and urographic phases) was performed on 20 patients with clear cell renal cell carcinoma and computed tomography texture analysis parameters such as entropy, kurtosis, skewness, mean, and standard deviation of pixel distribution were measured using multiple filter settings. These quantitative data were correlated with the expression of selected microRNAs (miR-21-5p, miR-210-3p, miR-185-5p, miR-221-3p, miR-145-5p). Both the evaluations (microRNAs and computed tomography texture analysis) were performed on matched tumor and normal corticomedullar tissues of the same patients cohort. Results: In this pilot study, we evidenced that computed tomography texture analysis has robust parameters (eg, entropy, mean, standard deviation) to distinguish normal from pathological tissues. Moreover, a higher coefficient of determination between entropy and miR-21-5p expression was evidenced in tumor versus normal tissue. Interestingly, entropy and miR-21-5p show promising correlation in clear cell renal cell carcinoma opening to a radiogenomic strategy to improve clear cell renal cell carcinoma management. Conclusion: In this pilot study, a promising correlation between microRNAs and computed tomography texture analysis has been found in clear cell renal cell carcinoma. A clear cell renal cell carcinoma can benefit from noninvasive evaluation of texture parameters in adjunction to biopsy results. In particular, a promising correlation between entropy and miR-21-5p was found

Multiple double-exchange mechanism by Mn2+^{2+}-doping in manganite compounds

Double-exchange mechanisms in RE$_{1-x}$AE$_{x}$MnO$_{3}$ manganites (where RE is a trivalent rare-earth ion and AE is a divalent alkali-earth ion) relies on the strong exchange interaction between two Mn$^{3+}$ and Mn$^{4+}$ ions through interfiling oxygen 2p states. Nevertheless, the role of RE and AE ions has ever been considered "silent" with respect to the DE conducting mechanisms. Here we show that a new path for DE-mechanism is indeed possible by partially replacing the RE-AE elements by Mn$^{2+}$-ions, in La-deficient La$_{x}$MnO$_{3-\delta}$ thin films. X-ray absorption spectroscopy demonstrated the relevant presence of Mn$^{2+}$ ions, which is unambiguously proved to be substituted at La-site by Resonant Inelastic X-ray Scattering. Mn$^{2+}$ is proved to be directly correlated to the enhanced magneto-transport properties because of an additional hopping mechanism trough interfiling Mn$^{2+}$-ions, theoretically confirmed by calculations within the effective single band model. The very idea to use Mn$^{2+}$ both as a doping element and an ions electronically involved in the conduction mechanism, has never been foreseen, revealing a new phenomena in transport properties of manganites. More important, such a strategy might be also pursed in other strongly correlated materials.Comment: 6 pages, 5 figure