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 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.

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 $N_f=2$.