Matrix probing and its conditioning

When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can be used to recover an approximation to A^-1. A basic question is whether this linear system is invertible and well-conditioned. In this paper, we show that if the Gram matrix of the B_j's is sufficiently well-conditioned and each B_j has a high numerical rank, then n {proportional} p log^2 n will ensure that the linear system is well-conditioned with high probability. Our main application is probing linear operators with smooth pseudodifferential symbols such as the wave equation Hessian in seismic imaging. We demonstrate numerically that matrix probing can also produce good preconditioners for inverting elliptic operators in variable media

LWFA With Low Energy Raman Seeded Pulses

Analytical and numerical calculations of plasma wakefield excitation and particle acceleration by Raman seeded laser pulse in self-modulation regime are presented. We derive energy threshold for self-modulation of diffraction-limited pulses. The parameter range where the Raman seeded amplitude plays an important role is investigated. We show that the seeded amplitude provides a coherent control mechanism for the phase of the wakefield wave. We show that with the use of Raman seed self-modulated wakefield acceleration is achievable for the pulses of intensities much lower than those typically used in the experiments. In particular, our 2D particle-in-cell simulations show that 30 mJ pulse combined with Raman seeded pulse, which is 1% in intensity of the main pulse is capable of generating similar to1 nC of relativistic electrons.Physic

The Lattice Free Energy with Overlap Fermions: A Two-Loop Result

We calculate the 2-loop partition function of QCD on the lattice, using the Wilson formulation for gluons and the overlap-Dirac operator for fermions. Direct by-products of our result are the 2-loop free energy and average plaquette. Our calculation serves also as a prototype for further higher loop calculations in the overlap formalism. We present our results as a function of a free parameter $M_0$ entering the overlap action; the dependence on the number of colors $N$ and fermionic flavors $N_f$ is shown explicitly.Comment: 10 pages, 5 figures. Final version to appear in Physical Review D. A missing overall factor was inserted in Eq. 12; it affects also Eq. 1

Renormalization scheme for a multi-qubit-network

We present a renormalization scheme which simplifies the dynamics of an important class of interacting multi-qubit systems. We show that a wide class of M+1 qubit systems can be reduced to an equivalent n+1 qubit system with n equal to, or greater than, 2, for any M. Our renormalization scheme faithfully reproduces the overall dynamics of the original system including the entanglement properties. In addition to its direct application to atom-cavity and nanostructure systems, the formalism offers insight into a variety of situations ranging from decoherence due to a spin-bath with its own internal entanglement, through to energy transfer processes in organic systems such as biological photosynthetic units.Comment: 4 pages, 4 figure

Away-side azimuthal distribution in a Markovian parton scattering model

An event generator is constructed on the basis of a model of multiple scattering of partons so that the trajectory of a parton traversing a dense and expanding medium can be tracked. The parameters in the code are adjusted to fit the \Delta\phi azimuthal distribution on the far side when the trigger momentum is in the non-perturbative region, p_T(trigger)<4 GeV/c. The dip-bump structure for 1<p_T(assoc)<2.5 GeV/c is reproduced by averaging over the exit tracks of deflected jets. An essential characteristic of the model, called Markovian Parton Scattering (MPS) model, is that the scattering angle is randomly selected in the forward cone at every step of a trajectory that is divided into many discrete steps in a semi-classical approximation of the non-perturbative scattering process. Energy loss to the medium is converted to thermal partons which hadronize by recombination to give rise to the pedestal under the bumps. When extended to high trigger momentum with \pt(trigger) >8 GeV/c, the model reproduces the single-peak structure observed by STAR without invoking any new dynamical mechanism.Comment: 20 pages + 3 figure