Weak Coupling Methods Research Articles

Molecular Dynamics Simulations With First Order Coupling to a Bath of Constant Chemical Potential

Abstract In molecular dynamics simulations the temperature or pressure can be controlled by applying a weak first-order coupling to a bath of constant temperature or pressure. This weak coupling technique to control system properties using a first-order relaxation equation is analyzed from a statistical mechanics point of view. It is shown, how the weak coupling scheme can be generalized and applied to a bath of contstant chemical potential. The presented method, to which in the following will be referred to as chemical potential weak coupling, is applied and tested on a Lennard-Jones fluid. The thermodynamic quantities known from the literature are accuratly reproduced. The temperature and chemical potential weak coupling methods aim to sample the canonical and grand canonical ensembles respectively. By analyzing the fluctuations in energy and number of particles, the tight relation between the ensembles and the distributions obtained from the weak coupling simulations is demonstrated. The influence of t...

Computing quark and gluon distribution functions for very large nuclei.

We argue that the distribution functions for quarks and gluons are computable at small x for sufficiently large nuclei, perhaps larger than can be physically realized. For such nuclei, we argue that weak coupling methods may be used. We show that the computation of the distribution functions can be recast as a many body problem with a modified propagator, a coupling constant which depends on the multiplicity of particles per unit rapidity per unit area, and for non-abelian gauge theories, some extra media dependent vertices. We explicitly compute the distribution function for gluons to lowest order, and argue how they may be computed in higher order.

On the Eichten-Preskill proposal for lattice chiral gauge theories

We have studied the Eichten-Preskill proposal for constructing lattice chiral gauge theories using both strong and weak coupling methods. The results indicate that this proposal is unlikely to work due to a dynamical behavior similar to that of the Smit-Swift proposal, which also does not give rise to chiral fermions.

Pairing instabilities of the extended Hubbard model for Cu-O-based superconductors.

We use weak-coupling methods to calculate the effective interaction between quasiparticles induced by charge and spin fluctuations in a three-band model for the copper-oxide superconductors with both intersite and intrasite repulsion. The instabilities to superconducting states of different symmetries are calculated; besides the d-wave superconductivity near the antiferromagnetic instability, we find that extended s-wave superconductivity is favored by a charge transfer resonance close to a valence instability. A phase diagram similar to experiments is obtained.

Collective excitations in the normal state of Cu-O-based superconductors.

Standard weak-coupling methods are used to calculate the excitation spectrum and the instabilities of the metallic phase of a three-band model for the copper-oxide superconductors with both intra- and intersite repulsion. Besides the magnetic excitations, a strong charge-transfer resonance of ${A}_{1g}$ symmetry is predicted. For reasonable parameters, the metallic phase is found to be unstable to a charge-transfer instability at large deviations from half filling, and at small deviations to an antiferromagnet.

Resonance enhancement of electron collision rates for fluorinelike ions

The distorted-wave approximation and similar weak-coupling methods are frequently used to calculate electron collision cross sections for studies of astrophysical and laboratory plasmas. Autoionizing resonances neglected in these approximations can significantly enhance the calculated rates for collisional excitation of some transitions in highly charged ions. We investigated the effects of such resonances on the excitation rates for n=2 to n=2 transitions in fluorinelike Fe, Se, Mo, Ag, Xe, and Eu. The background excitation rates were calculated using a relativistic distorted-wave approximation, and the detailed Auger and radiative rates were calculated using a multiconfiguration Dirac-Fock model. The largest effect is on the electric-dipole-forbidden transitions. The enhancement diminishes with increasing atomic number for all transitions.

A phenomenology of QCD on a small lattice

Weak-coupling methods, appropriate to a small lattice, reproduce many features of the QCD spectrum derived on a 6 3 × 10 lattice using Monte Carlo techniques and offer some insight into finite lattice size effects.

Ein neuer Variationsansatz f�r das Polaron

A new trial function for the self-energy of the polaron is presented which is a combination of the weak and strong coupling methods ofLee,Low andPines resp.Pekar. The result for the ground-state energy is a smooth interpolation between both methods which is better than either one but not as good asFeynman's result.