On Factorization of Molecular Wavefunctions

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$\Phi$\} of the molecular Schr\"odinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $\Phi$ in the form $\varphi\chi$ where $\chi$ is \textit{purely} a function of the nuclear coordinates, while $\varphi$ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be achieved in this form with $\varphi$ and $\chi$ interpretable as `electronic' and `nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.Comment: Manuscript submitted to Journal of Physics A: Mathematical and Theoretical, May 2015. Accepted for Publication August 24 201

The impact of contractual savings institutions on securities markets

The authors assess empirically the impact of contractual savings institutions portfolios (pension funds and life insurance companies) on securities markets, for example, depth and liquidity in the domestic stock market, and depth in the domestic bond market. They discuss how the institutionalization of savings can modify financial markets through the lengthening of securities'maturities. The results are the following: 1) An increase in assets of contractual savings institutions relative to domestic financial assets has a positive impact on the depth of stock and bond markets on average. 2) The impact on stock market depth and liquidity is nonlinear: it is stronger in countries where corporate information is more transparent. 3) There is evidence of a significant heterogeneity among countries: contractual savings have a stronger impact on securities markets in countries where the financial system is market based, pension fund contributions are mandatory, and international transactions in securities are lower. 4) The authors do not find that the impact of contractual savings institutions on securities markets is explained by the overall level of development, education, demographic structure or the legal environment.Economic Theory&Research,Insurance&Risk Mitigation,Banks&Banking Reform,Payment Systems&Infrastructure,Insurance Law,Insurance&Risk Mitigation,Banks&Banking Reform,Financial Intermediation,Economic Theory&Research,Insurance Law

A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods

We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the method (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes, obtaining as a by-product an explicit lifting operator close to the ones used in some theoretical studies of the Mimetic Finite Difference scheme. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme

Contractual savings, capital markets, and firms'financing choices

The authors analyze the relationship between the development and asset allocation of contractual savings and firms'capital structures. The authors develop a simple model of firms'leverage and debt maturity decisions. They illustrate the mechanisms through which contractual savings development may affect corporate financing patterns. In the empirical section, the authors show that the development and asset allocation of contractual savings have an independent impact on firms'financing choices. Different channels are identified. In market-based economies, an increase in the proportion of shares in the portfolio of contractual savings leads to a decline in firms'leverage. In bank-based economies, instead, an increase in the size of contractual savings is associated with an increase in leverage and debt maturity in the corporate sectorBanks&Banking Reform,Payment Systems&Infrastructure,International Terrorism&Counterterrorism,Economic Theory&Research,Financial Intermediation,Banks&Banking Reform,Economic Theory&Research,Financial Intermediation,Environmental Economics&Policies,International Terrorism&Counterterrorism

Contractual savings institutions and banks'stability and efficiency

The authors analyze the relationship between the development of contractual savings institutions and banks'efficiency, credit, and liquidity risks. They discuss the potential mechanisms through which the development of contractual savings institutions may affect the banking sector. They show that the development of contractual savings institutions has a significant impact on bank spreads and loan maturity. After controlling for banks'characteristics, macroeconomic factors, and more standard indicators of financial development, they show that the development of contractual savings institutions is associated with increased efficiency of the banking system and greater resilience to credit and liquidity risks.Payment Systems&Infrastructure,Banks&Banking Reform,Economic Theory&Research,Financial Intermediation,Insurance&Risk Mitigation,Contractual Savings,Banks&Banking Reform,Financial Intermediation,Economic Theory&Research,Insurance&Risk Mitigation

Origin of Second Harmonic Generation from individual Silicon Nanowires

We investigate Second Harmonic Generation from individual silicon nanowires and study the influence of resonant optical modes on the far-field nonlinear emission. We find that the polarization of the Second Harmonic has a size-dependent behavior and explain this phenomenon by a combination of different surface and bulk nonlinear susceptibility contributions. We show that the Second Harmonic Generation has an entirely different origin, depending on whether the incident illumination is polarized parallel or perpendicularly to the nanowire axis. The results open perspectives for further geometry-based studies on the origin of Second Harmonic Generation in nanostructures of high-index centrosymmetric semiconductors.Comment: 7 Pages, 4 Figures + 3 Pages, 6 Figures in Appendi

Capturing coevolutionary signals in repeat proteins

The analysis of correlations of amino acid occurrences in globular proteins has led to the development of statistical tools that can identify native contacts -- portions of the chains that come to close distance in folded structural ensembles. Here we introduce a statistical coupling analysis for repeat proteins -- natural systems for which the identification of domains remains challenging. We show that the inherent translational symmetry of repeat protein sequences introduces a strong bias in the pair correlations at precisely the length scale of the repeat-unit. Equalizing for this bias reveals true co-evolutionary signals from which local native-contacts can be identified. Importantly, parameter values obtained for all other interactions are not significantly affected by the equalization. We quantify the robustness of the procedure and assign confidence levels to the interactions, identifying the minimum number of sequences needed to extract evolutionary information in several repeat protein families. The overall procedure can be used to reconstruct the interactions at long distances, identifying the characteristics of the strongest couplings in each family, and can be applied to any system that appears translationally symmetric

Quantum Non-Equilibrium Steady States Induced by Repeated Interactions

We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The two-point correlations are calculated exactly and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady state current, proportional to the difference in the reservoirs' magnetizations, shows a non-monotonous behavior with respect to the system-reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.Comment: to appear in Phys. Rev. Let

Ro-vibrational relaxation of HCN in collisions with He: Rigid bender treatment of the bending-rotation interaction

We present a new theoretical method to treat atom-rigid bender inelastic collisions at the Close Coupling level (RBCC) in the space fixed frame. The coupling between rotation and bending is treated exactly within the rigid bender approximation and we obtain the cross section for the rotational transition between levels belonging to different bending levels. The results of this approach are compared with those obtained when using the rigid bender averaged approximation (RBAA) introduced in our previous work dedicated to this system. We discuss the validity of this approximation and of the previous studies based on rigid linear HCN