Reliability Assessment for Large-Scale Molecular Dynamics Approximations

Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems, however, create the need for approximations to the standard MD methods and for uncertainty quantification and reliability assessment of those approximations. In this paper, we exploit the intrinsic two-scale nature of MD to construct a class of large-scale dynamics approximations. The reliability of these methods are evaluated here by measuring the differences between full, classical MD simulations and those based on these large-scale approximations. Molecular dynamics evolutions are non-linear and chaotic, so the complete details of molecular evolutions cannot be accurately predicted even using full, classical MD simulations. This paper provides numerical results that demonstrate the existence of computationally efficient large-scale MD approximations which accurately model certain large-scale properties of the molecules: the energy, the linear and angular momenta, and other macroscopic features of molecular motions.Comment: 16 pages, 12 figure

Coarse grained NN potential with Chiral Two Pion Exchange

We determine the chiral constants of the Nucleon-Nucleon Two Pion Exchange potential deduced from Chiral Perturbation Theory. By using a coarse grained representation of the short distance interactions with 30 parameters, the Partial Wave Analysis fit gives chi^2/dof = 1.1 to a mutually consistent set of 6713 data previously built from all published proton-proton and neutron proton scattering data from 1950 till 2013 with LAB energy below 350 MeV. We obtain (c1, c3, c4)=(-0.41+- 1.08,-4.66+- 0.60, 4.31+- 0.17)/GeV with an almost 100% anti-correlation between c1 and c3. We also provide the errors in the short distance parameters and propagate them to the deuteron properties and low partial waves phase shifts.Comment: 11 pages, 7 figures, 11 tables. Enlarged versio

Nuclear Binding Energies and NN uncertainties

There is an increasing interest in quantifying the predictive power in nuclear structure calculations. We discuss how both experimental and systematic errors at the NN-level can be used to estimate the theoretical uncertainties by rather simple means and without solving the full nuclear many body problem. We emphasize the role of effective interactions defined by coarse graining the NN potential to length scales of the order of the minimal de Broglie wavelength probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim 0.1 - 0.4MeV for the binding energy per particle throughout the periodic table for 2 \leq A \leq 208, and a linear growth of the error with density for nuclear matter \DeltaB/A \sim 3.75{\rho}n.m. and neutron matter \DeltaB/N \sim 3.5{\rho}n.. This suggests to limit the computational effort in solving the Nuclear Many Body Problem to such an accuracy.Comment: 6 pages. 2 figures. Presented by RNP at Sixth International Conference on Quarks and Nuclear Physics, April 16-20, 2012. Ecole Polytechnique, Palaiseau, Paris, Franc

Error Analysis of Nuclear Matrix Elements

We estimate the expected errors of nuclear matrix elements coming from the uncertainty on the NN interaction. We use a coarse grained (GR) interaction fitted to NN scattering data, with several prescriptions for the long-part of the interaction, including one pion exchange and chiral two-pion exchange interactions.Comment: Presented at the 22th European Conference On Few-Body Problems In Physics: EFB22 9 - 13 Sep 2013, Krakow (Poland

Low energy chiral two pion exchange potential with statistical uncertainties

We present a new phenomenological Nucleon-Nucleon chiral potential fitted to 925 pp and 1743 np scattering data selected from the Granada-2013 NN-database up to a laboratory energy of $125$ MeV with 20 short distance parameters and three chiral constants $c_1$, $c_3$ and $c_4$ with $\chi^2/\nu = 1.02$. Special attention is given to testing the normality of the residuals which allows for a sound propagation of statistical errors from the experimental data to the potential parameters, phase-shifts, scattering amplitudes and counter-terms. This fit allows for a new determination of the chiral constants $c_1$, $c_3$ and $c_4$ compatible with previous determinations from NN data. This new interactions is found to be softer than other high quality potentials by undertaking a Weinberg eigenvalue analysis. We further explore the interplay between the error analysis and the assumed form of the short distance interaction. The present work shows that it is possible to fit NN scattering with a TPE chiral potential fulfilling all necessary statistical requirements up to 125 MeV and shows unequivocal non-vanishing D-wave short distance pieces.Comment: 16 pages, 10 figures, 5 tables. Enlarged version including Weinberg eigenvalue analysis and cut-off dependenc

Effective interactions in the delta-shells potential

We determine two-body Skyrme force parameters from a Nucleon-Nucleon interaction as a function of the maximal momentum fitting NN scattering data. We find general agreement with Vlowk interactions based on high quality potentials.Comment: 4 page, 1 figure, Presented by R.N.P. at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japa

Solution for the dispersive and dissipative atom-field Hamiltonian under time dependent linear amplification processes

The dispersive interaction between a two-level atom and a quantized field is studied. We consider besides a time dependent linear amplification and dissipative processes. In order to solve the master equation for this system, we use superoperator techniques

Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold

Using the delta-shell representation we present a successful fit to neutron-proton and proton-proton scattering data below pion production threshold. A detailed overview of the theory necessary to calculate observables with this potential is presented. A new data selection process is used to obtain the largest mutually consistent data base. The analysis includes data within the years 1950 to 2013. Using 46 parameters we obtain chi^2/Ndata = 1.04 with Ndata = 6713 including normalization data. Phase shifts with error bars are provided.Comment: 32 pages, 1 figure, 10 table

Statistical Error analysis of Nucleon-Nucleon phenomenological potentials

Nucleon-Nucleon potentials are commonplace in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard least squares fitting procedure and apply, along with more conventional tests, a tail sensitive quantile-quantile test as a simple and confident tool to verify the normality of residuals. We show that the fulfilment of normality tests is linked to a judicious and consistent selection of a nucleon-nucleon database. These considerations prove crucial to a proper statistical error analysis and uncertainty propagation. We illustrate these issues by analyzing about 8000 proton-proton and neutron-proton scattering published data. This enables the construction of potentials meeting all statistical requirements necessary for statistical uncertainty estimates in nuclear structure calculations.Comment: 20 pages. 13 figures. 10 tables, (minor numerical changes) Physical Review C (to appear

Three pion nucleon coupling constants

There exist four pion nucleon coupling constants, $f_{\pi^0, pp}$, $-f_{\pi^0, nn}$, $f_{\pi^+, pn} /\sqrt{2}$ and $f_{\pi^-, np} /\sqrt{2}$ which coincide when up and down quark masses are identical and the electron charge is zero. While there is no reason why the pion-nucleon-nucleon coupling constants should be identical in the real world, one expects that the small differences might be pinned down from a sufficiently large number of independent and mutually consistent data. Our discussion provides a rationale for our recent determination $$f_p^2 = 0.0759(4) \, , \quad f_{0}^2 = 0.079(1) \,, \quad f_{c}^2 = 0.0763(6) \, ,$$ based on a partial wave analysis of the $3\sigma$ self-consistent nucleon-nucleon Granada-2013 database comprising 6713 published data in the period 1950-2013.Comment: 15 pages, 6 figures. Invited talk at the Workshop on Determination of the Fundamental Parameters in QCD, Mainz Institute of Theoretical Physics, Johannes Gutenberg University of Mainz. Corrected Version matching publication in Mod. Phys. Lett.