We show that the nature of the topological fluctuations in $SU(3)$ gauge theory changes drastically at the finite temperature phase transition. Starting from temperatures right above the phase transition topological fluctuations come in well separate
d lumps of unit charge that form a non-interacting ideal gas. Our analysis is based on a novel method to count not only the net topological charge, but also separately the number of positively and negatively charged lumps in lattice configurations using the spectrum of the overlap Dirac operator. This enables us to determine the joint distribution of the number of positively and negatively charged topological objects, and we find this distribution to be consistent with that of an ideal gas of unit charged topological objects.
We study the finite temperature localization transition in the spectrum of the overlap Dirac operator. Simulating the quenched approximation of QCD, we calculate the mobility edge, separating localized and delocalized modes in the spectrum. We do thi
s at several temperatures just above the deconfining transition and by extrapolation we determine the temperature where the mobility edge vanishes and localized modes completely disappear from the spectrum. We find that this temperature, where even the lowest Dirac eigenmodes become delocalized, coincides with the critical temperature of the deconfining transition. This result, together with our previously obtained similar findings for staggered fermions shows that quark localization at the deconfining temperature is independent of the fermion discretization, suggesting that deconfinement and localization of the lowest Dirac eigenmodes are closely related phenomena.
Across the finite temperature transition to the quark-gluon plasma, the QCD topological susceptibility decreases sharply. Thus in the high temperature phase the remaining topological objects (possibly calorons) form a weakly interacting dilute gas. T
he overlap Dirac operator, through its exact zero modes, allows one to measure the net topological charge. We show that separately the number of positively and negatively charged topological objects can also be extracted from the low end of the overlap Dirac spectrum. We find that slightly above the phase transition their number distributions are already consistent with an ideal gas of non-interacting topological objects.
At high temperature part of the spectrum of the quark Dirac operator is known to consist of localized states. This comes about because around the crossover temperature to the quark-gluon plasma localized states start to appear at the low end of the s
pectrum and as the system is further heated, states higher up in the spectrum also get localized. Since localization and the crossover to the chirally restored phase happen around the same temperature, the question of how the two phenomena are connected naturally arises. Here we speculate on the nature of possible gauge configurations that could support localized quark eigenmodes. In particular, by analyzing eigenmodes of the staggerd and overlap Dirac operator we show that the dilute gas of calorons in the high temperature phase is very unlikely to play a major role in localization.
We investigate the fracture of heterogeneous materials occurring under unloading from an initial load. Based on a fiber bundle model of time dependent fracture, we show that depending on the unloading rate the system has two phases: for rapid unloadi
ng the system suffers only partial failure and it has an infinite lifetime, while at slow unloading macroscopic failure occurs in a finite time. The transition between the two phases proved to be analogous to continuous phase transitions. Computer simulations revealed that during unloading the fracture proceeds in bursts of local breakings triggered by slowly accumulating damage. In both phases the time evolution starts with a relaxation of the bursting activity characterized by a universal power law decay of the burst rate. In the phase of finite lifetime the initial slowdown is followed by an acceleration towards macroscopic failure where the increasing rate of bursts obeys the (inverse) Omori law of earthquakes. We pointed out a strong correlation between the time where the event rate reaches a minimum value and of the lifetime of the system which allows for forecasting of the imminent catastrophic failure.
We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD
. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperature. We discuss how these problems can be solved by two new techniques, the first one with reweighting using the quark zero modes and the second one with the integration method.
The $Theta_{eff}/Theta_{rig}$ parameter of the spin distribution of the level density was determined for 61 nuclei covering the mass range of 44 to 200. The experimental isomeric cross-section ratios for 25 isomeric pairs were compared with the model
calculation to find the best fit to the experimental data. The model calculations were carried out with the TALYS code using the BSFG model for the level density. The reduced $chi ^2$ values were calculated to describe the deviation of the experimental data from the model calculation. An $eta_d $ was introduced calculating the $Theta_{eff}/Theta_{rig}$ value from the low energy discrete levels of the nucleus. The $eta /eta_d $ values seem to be independent of the mass number, their average value near to one. The $eta /eta_d $ values also seem to be independent of the average excitation energy in the continuum, indicating that $eta $ is independent of the excitation energy. The mass number and (N-Z) dependence of the $eta $ values were studied. The $eta $ values for the nuclei with odd mass number show an exponential decrease as a function of A or (N-Z). The $eta $ values for the odd-odd type of nuclei appear to be constant, near one, up to the mass number 110 or (N-Z) of 13. Above these values, the $eta $ values show exponential decrease. The $eta $ values for even-even type nuclei decrease exponentially up to A equal to 142 or (N-Z) equal to 20. The values are lower than those for the nearby odd-odd type nuclei. The $eta $ values increase for nuclei with A between 142 and 156 and (N-Z) between 20 and 28, and they finally reach the value of odd-odd type systematics.
