Grid Finite Temperature Qcd In The Su (3) Glueball Spectrum Of Qcd Phase Transition, And Sd-pair Shell Model Excitation Spectrum Of The Nature And Shape Of The Phase Transition Of Nuclear Low

In this dissertation,two main research subjects are concerned,Lattice Quantum Chromodynamics and SD-pair shell model.The QCD at finite temperature and finite density,especially QCD phase-transition, has been an distinguished area,for the close relation with RHIC,LHC and Anstro-particle physics.However,in the QCD critical region(T∈[100,300]MeV), quark-gluon systems are still strong interacting,so traditional purtabtive method can't work well here.The numerical Lattice QCD starting from first principle is considered as the best theory to give reliable results.With lattice QCD,we mainly talk about two works connected with QCD phase transition and QGP closely.First,thermal properties of the quenched SU(3) glueballs are investigated in a large temperature range from 0.3T_c to 1.9T_c on anisotropic lattices.The glueball operators are optimized for the projection of the ground states by the variational method with a smearing scheme. Their thermal correlators are calculated in all 20 symmetry channels.It is found in all channels that the pole masses M_G of glueballs remain almost constant when the temperature is approaching to the critical temperature T_c from the below,and start to reduce gradually with the temperature going above T_c.The correlators in the 0⁺⁺, 0^-+,and 2⁺⁺ channels are also analyzed based on the Breit-Wigner ansatz by assuming a thermal widthΓto the pole massω₀ of each thermal glueball ground state. While the values ofω₀ are insensitive to T in the whole temperature range,the thermal widthsΓexhibit distinct behaviors at temperatures below and above T_c.The widths are very small(approximately few percents ofω₀ or even smaller) when T＜T_c,but grow abruptly when T＞T_c and reach values of roughlyΓ～ω₀/2 at T≈1.9T_c. Secondly,QCD at non-zero baryon density is expected to have a critical point where the zero-density cross-over turns into a first order phase transition.To identify this point we scan the density-temperature space using a canonical ensemble method.For a given temperature,we plot the chemical potential as a function of density looking for a "S-shape" as a signal for a first order transition.We carried out simulations using Wilson fermions with m_π≈1GeV on 6³Ã—4 lattices.As a benchmark,we ran four flavors simulations where we observe a clear signal.In the two flavors case we do not see any signal for temperatures as low as 0.83T_c.The nucleon-pair shell model,truncated to an SD subspace,is applied to 1^126-134Xe and ^128-136Ba.The spectra,eigenstates,and electromagnetic transition strengths of these nuclei,which are known to display O(6).symmetry,are described in terms of a three-parameter Hamiltonian.Agreement with experiment is good,in particular, mixed-symmetry configurations and the upward shift and fragmentation of the M1 strength with increasing neutron numbers emerges naturally.The results show that the SD subspace approximation improves with the number of pairs.On the other hand, Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the SD-pair shell model.The results show that some transitional patterns in the SD-pair shell model are similar to the U(5)-SU(3),U(5)-SO(6) transitions with signatures of the critical point symmetry of the interacting boson model.