Electronic properties and polaronic dynamics of semi-Dirac system within ladder approximation

We investigate the electronic properties of the semi-Dirac system and its polaronic dynamics when coupled with a fermi bath with quadratic dispersion. The electronic anisotropic transport properties and the semiclassical dynamics of the semi-Dirac system are studied, including the density-of-states, conductivity, transport relaxation rate, specific heat, electrical current denity, and free energy. The attractive polaron formed as the semi-Dirac impurity dressed with the particle-hole excitations in a two-dimensional system are studied both analytically and numerically. The pair propagator, self-energy, spectral function are being detailly calculated and discussed.