We study electric, thermal, and thermoelectric conductivities in the vicinity of a z = 2 superconductor-diffusive metal transition in two dimensions, both in the high and low frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to st...

Recently, the free energy of the target space mean field (TSMF) matrix model has been calculated in the low temperature phase, order-by-order in a low temperature expansion. The TSMF model is a matrix model whose discrete target space has an infinite coordination number, and whose free energy assumes a universal form, corresponding to baby universes joined into a tree. Here the free energy is s...

in this paper we studied the thermal negativity in a two-qubit xx spin ½ chain model and xxx spin1/2 chain model(isotropic heisenberg model)spin-1/2 chain subjected to an external magnetic field inz direction. we calculate analytical relation for the thermal negativity for two qubit xx and xxx spinchain models in the external magnetic field. effects of the magnetic field and temperature on then...