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

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

Instanton Contribution to the Proton and Neutron Electric Form Factors

We study the instanton contribution to the proton and neutron electric form factors. Using the single instanton approximation, we perform the calculations in a mixed time-momentum representation in order to obtain the form factors directly in momentum space. We find good agreement with the experimentally measured electric form factor of the proton. For the neutron, our result falls short of the experimental data. We argue that this discrepancy is due to the fact that we neglect the contribution of the sea quarks. We compare to lattice calculations and a relativistic version of the quark-diquark model.Comment: 8 pages, 5 figures, updated references, to appear in Phys. Lett.

Gaussian quantum fluctuations in the superfluid-Mott phase transition

Recent advances in cooling techniques make now possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gappless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for next future experiments on quantum phase transitions.Comment: 7 pages, 4 figures, to be published in Physical Review