Lattice Quantum Chromodynamics

Lattice structure offers the potential to produce desirable macro-scale material properties for a wide variety of engineering applications including blast and impact protection system, thermal insulation, structural aircraft and vehicle components body implants. The work presented here to study the characteristics of quasistatic and dynamic behaviour of lattice structure of different materials. Initially cuboidal lattice structures were investigated to study the stress-strain response, failure behaviour and energy absorbing capacity. Drop hammer test were carried out to understand the behaviour of lattice structures under dynamic behaviour. The results obtained shows quasistatic tests are agreeable with dynamic tests.

We study the meta-stable states in high temperature phase of QCD characterised by nonzero expectation values for the imaginary part of the Polyakov loop. We consider $N_f= 2, 3$ dynamical staggered quarks, and carry out simulations at various values of the coupling $\beta$ to observe these states. In particular, we find the value of the coupling ($\beta_m$) above which the meta-stable states appear. The resulting value of $\beta_m$ corresponds to temperature $T_m \gtrsim 750$MeV for $N_f=2$.

We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with $Z_4$ noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a $16^3 \times 24$ quenched lattice at $\beta = 6.0$ for Wilson fermions with $\kappa=0.154, 0.155$, and $0.1555$ which correspond to pion masses at $650, 538$, and $478$ MeV, respectively. The chirally extrapolated $u$ and $d$ quark momentum/angular momentum fraction is found to be $0.64(5)/0.70(5)$, the strange momentum/angular momentum fraction is $0.023(6)/0.022(7)$, and that of the glue is $0.33(6)/0.28(8)$. The previous study of quark spin on the same lattice revealed that it carries a fraction of $0.25(12)$ of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes $0.47(13)$ of the proton spin with almost all of it coming from the disconnected insertions.

The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector. In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector.

We study the strangeness contribution to nucleon matrix elements using N f = 2 + 1 dynamical clover fermion configurations generated by the CP-PACS/JLQCD collaboration. In order to evaluate the disconnected insertion (DI), we use the Z(4) stochastic method, along with unbiased subtraction from the hopping parameter expansion which reduces the off-diagonal noises in the stochastic method. Furthermore, we find that using many nucleon sources for each configuration is effective in improving the signal. Our results for the quark contribution to the first moment x q in the DI, and the strangeness magnetic moment show that the statistical errors are under control with these techniques. We also study the gluonic contribution to the nucleon using the overlap operator to construct the gauge field tensor, F µν . The application to the calculation of first moment, x G , gives a good signal in quenched lattice QCD.