arXiv subjects

I. T. Drummond

Publications and source records attributed to I. T. Drummond.

23 records · Page 2Linked to original sources

arXiv1997

Effective drift and diffusivity in non-Gaussian random gradient flows

We study the long-range effective drift and diffusivity of a particle in a random medium moving subject to a given molecular diffusivity and a local drift. The local drift models the effect of a random electrostatic field on a neutral but polarizable molecule. Although the electrostatic field is assumed to obey Gaussian statistics the induced statistics of the drift velocity field are non-Gaussian. We show that a four-loop perturbation theory calculation of the effective diffusivity is in rather good agreement with the outcome of a numerical simulation for a reasonable range of the disorder parameter. We also measure the effective drift in our simulation and confirm the validity of the ``Einstein relation'' that expresses the equality of the renormalization factors, induced by the random medium, for the effective drift and effective diffusivity, relative to their molecular values. The Einstein relation has previously only been confirmed for Gaussian random drift fields. The simulation result, for our non-Gaussian drift model, is consistent with a previous theoretical analysis showing the Einstein relation should remain true, independently of the precise character of the statistics of the drift velocity field.

cond-mat.dis-nn↗

arXiv1997

Upsilon Spectrum from NRQCD with Improved Action

We explore the effect of higher order operators in the non-relativistic formulation of QCD (NRQCD). We calculated masses in the b \bar b spectrum using quenched gauge configurations at beta = 6.0 and two different NRQCD actions which have been corrected to order mv^4 and mv^6. The two-point functions are calculated in a gauge invariant fashion. We find the general structure of the spectrum to be the same in the two cases. Using the P - 3S1 splitting we determine the inverse lattice spacings to be 2.44(4) GeV and 2.44(5) GeV for the mv^4 and mv^6 actions, respectively. We do observe shifts in the spin splittings. The hyperfine splitting is reduced by approximately 4 MeV, while the fine splitting is down by up to 10 MeV, albeit with large statistical errors.

hep-lat↗

arXiv1996

Eliminating Infrared Divergences in the Pressure

The pressure of a system in thermal equilibrium is expressed as a mass integral over a sum of thermal propagators. This allows a Dyson resummation and is used to demonstrate that potential infrared divergences are rendered harmless.

hep-th↗

arXiv1996

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.

cond-mat↗

arXiv1993

Radial Excited States for Heavy Quark Systems in NRQCD

Following the Non-Relativistic QCD approach we use a gauge invariant smearing method with factorization to measure the excitation energies for a heavy $Q\bar{Q}$ system on a $24^3\times 48$ lattice at $β=6.2$. The results come from averaging over an ensemble of 60 QCD configurations. In order to enhance the signal from each configuration we use wall sources for quark propagators. The quark Hamiltonian contains only the simplest non-relativistic kinetic energy term. The results are listed for a range of bare quark masses. The mass splittings are insensitive to this variable though there are a slight trends with increasing quark mass. For an appropriate choice of UV cut-off ($a^{-1}=3.2$Gev) the mass spectrum compares reasonably well with the experimental values for the spin-averaged energy gaps of the $Υ$ system. We also present results for the $DE$ and $DT$ waves for the lowest bare quark mass. The results are consistent with degeneracy between the two types of $D$ wave. This encourages the idea that even with our simple quark Hamiltonian the departure from rotational invariance is not great.

hep-lat↗