Spectral function of hadrons on finite temperature lattice QCD

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The spectral function of hadrons at finite temperature is expected to have rich physical contents, i.e., its mass and bound state under environment at finite temperature. Recently several authors have tried to determine the spectral function from propagators calculated by lattice QCD simulations. The problem is classified to an inverse problem of a linear equation, but it has ill-posed nature and hard to invert. We developed a new regularization scheme to find a spectral function by the use of truncated singular value decomposition and maximal entropy method. Our method always give a solution which satisfies the positivity requirement for the spectral function. We applied the method to lattice date with temporal lattice size Nt=20 and analyzed pseudo scalar and vector channels. On our lattice, Nt=20 corresponds to temperature just before the QCD phase transition. There are several definitions of entropy. We tried two definitions and the results are consistent.The data used in this analysis are made under quenched approximation and do not contain dynamical fermion effects. The treatment of fermions on the lattice is difficult because of its doubling problem. We developed a new algorithm for the lattice fermion which has less species than the standard fermion. We also made the feasibility study of the method.A system for the data analysis was introduced in this project. By the use of the system, we also made simulations of Nelson's quantum stochastic process and estimated tunneling time of the electron through magnetic thin films.