Molecular Dynamics at Low Time Resolution

The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale, in order not to cut-off important physical effects. We show that, in systems obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs at time scales smaller than dt can be analytically integrated out and gives raise to a time-dependent correction to the diffusion coefficient, which we rigorously compute. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps dt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy-model and the denaturation of a protein.Comment: 12 pages, 5 figure

CKM matrix: the `over-consistent' picture of the unitarity triangle

In presenting an up-to-date account of the experimental knowledge of the CKM matrix, special emphasis is placed on the exceptional degree of consistency shown by the current Standard Model determination of the unitarity triangle; some implications in the question of how the theoretical nature of the dominant uncertainties affects the Standard Model predictions are discussed. Recent experimental results include improved determinations of |V_{cb}| by OPAL and CLEO, the confirmation of rare (charmless hadronic and electromagnetic penguin) B decays and preliminary sin(2 beta) measurements by BaBar and Belle (new world average: sin(2 beta) = 0.48 +0.22 -0.24). The updated constraints lead to the Standard Model predictions sin(2 beta) = 0.68 +/- 0.03(exp) +/- 0.04(th), sin(2 alpha) = -0.43 +/- 0.15(exp) +/- 0.20(th), gamma = 56 +/- 5(exp)(+5 -6)(th) deg, Delta m_{Bs} = 16.2 (+2.7 -0.3)(exp)(+1.5 -1.0)(th) ps^{-1}.Comment: Contribution to Beauty 2000, September 13-18 2000, Kibbutz Maagan, Israel; to appear in the Proceedings (Nucl. Instr. Meth. A). LaTeX, 8 pages with 4 figures. Revisions: fixed two references; other minor correction

Instanton-Induced Correlations in Hadrons

QCD instantons generate non-perturbative spin- and flavor- dependent forces between quarks. We review the results of a series of studies on instanton-induced correlations in hadrons. We first present some evidence for instanton-mediated interactions in QCD, based on lattice simulations. Then we show that the Instanton Liquid Model can reproduce the available data on proton and pion form factors at large momentum transfer and explain the delay of the onset of the perturbative regime in several hard reactions. We also show that instantons generate a deeply bound scalar color anti-triplet diquark, with a mass of about 450 MeV and size comparable with that of the proton. The strong attraction in the anti-triplet scalar diquark channel leads to a quantitative description of non-leptonic weak decays of hyperons and provides a microscopic dynamical explanation of the Delta I=1/2 rule.Comment: Summary of the results presented at the "8th Workshop on Non-perturbative Quantum Chromodynamics", Paris 7-11 June 2003, the "26th International School on Nuclear Physics", Erice 16-24 September 2004, and the "X Convegno sui Problemi della Fisica Nucleare Teorica", Cortona, 6-9 October 200

Transition Path Theory from Biased Simulations

Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q^+(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first, we further extend the recently introduced Self-Consistent Path Sampling (SCPS) algorithm in order to compute the committor q^+(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.Comment: Version accepted for publication in J. Chem. Phy