Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results

Recently a local mean field theory for both eqilibrium and transport properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77, 165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to the results of dynamic Monte Carlo simulations. In a thermal equilibrium state we compare the density of states and the occupation probabilities. We also study the transition rates between different states and find that the mean field rates underestimate a certain class of important transitions. We propose modified rates to be used in the mean field approach which take into account correlations at the minimal level in the sense that transitions are only to take place from an occupied to an empty site. We show that this modification accounts for most of the difference between the mean field and Monte Carlo rates. The linear response conductance is shown to exhibit the Efros-Shklovskii behaviour in both the mean field and Monte Carlo approaches, but the mean field method strongly underestimates the current at low temperatures. When using the modified rates better agreement is achieved

Gluon structure function for deeply inelastic scattering with nucleus in QCD

In this talk we present the first calculation of the gluon structure function for nucleus in QCD. We discuss the Glauber formula for the gluon structure function and the violation of this simple approach that we anticipate in QCD. (Talk given by E. Levin at QCD and nuclear target session at the Workshop on Deep Inelastic Scattering and QCD, Paris, April 1995).Comment: 10 pages(latex file),4 fig (eps.files

Why charges go to the surface: a generalized Thomson problem

We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes

Gluon density in nuclei

In this talk we present our detail study ( theory and numbers) [1] on the shadowing corrections to the gluon structure functions for nuclei. Starting from rather contraversial information on the nucleon structure function which is originated by the recent HERA data, we develop the Glauber approach for the gluon density in a nucleus based on Mueller formula [2] and estimate the value of the shadowing corrections in this case. Than we calculate the first corrections to the Glauber approach and show that these corrections are big. Based on this practical observation we suggest the new evolution equation which takes into account the shadowing corrections and solve it. We hope to convince you that the new evolution equation gives a good theoretical tool to treat the shadowing corrections for the gluons density in a nucleus and, therefore, it is able to provide the theoretically reliable initial conditions for the time evolution of the nucleus - nucleus cascade.Comment: Talk at RHIC'96, 43 pages, 23 figure

Measuring the saturation scale in nuclei

The saturation momentum seeing in the nuclear infinite momentum frame is directly related to transverse momentum broadening of partons propagating through the medium in the nuclear rest frame. Calculation of broadening within the color dipole approach including the effects of saturation in the nucleus, gives rise to an equation which describes well data on broadening in Drell-Yan reaction and heavy quarkonium production.Comment: 11 pages, 5 figures, based on the talk presented by B.K. at the INT workshop "Physics at a High Energy Electron Ion Collider", Seattle, October 200

Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations.Comment: 6 pages, 1 figur

Scaling violation and shadowing corrections at HERA

We study the value of shadowing corrections (SC) in HERA kinematic region in Glauber - Mueller approach. Since the Glauber - Mueller approach was proven in perturbative QCD in the double logarithmic approximation (DLA), we develop the DLA approach for deep inelastic structure function which takes into account the SC. Our estimates show small SC for $F_2$ in HERA kinematic region while they turn out to be sizable for the gluon structure function. We compare our estimates with those for gluon distribution in leading order (LO) and next to leading order (NLO) in the DGLAP evolution equations.Comment: 9pp,6 figures in eps file

Coulomb Drag for Strongly Localized Electrons: Pumping Mechanism

The mutual influence of two layers with strongly loclized electrons is exercised through the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage drop in the passive layer, when a current is passed through the active layer. We find that the microscopic origin of drag lies in the time correlations of the occupation numbers of the sites involved in a hop. These correlations are neglected within the conventional Miller-Abrahams scheme for calculating the hopping resistance.Comment: 5 pages, 3 figure