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Electronic viscosity in a multiple quantum well system

We calculate the electronic viscosity for a multiple quantum well structure in the presence of disorder potential(V = 4 meV), the electron-electron repulsion(U = 5-17 meV) and a strong magnetic field (B greater than or equal to 16.5 T) in the direction in which the electrons are trapped. This viscosity is different from the dissipation-less Hall viscosity which cannot take non-zero value in a time reversal invariant system. The Fermi energy density of states for the system has been calculated in the t-matrix approximation assuming low concentration of impurities. Our approach involves calculation of the density of viscosity, for temperature close to 0 K, on the Brillouin zone(BZ) followed by the numerical evaluation of the integral of viscosity density over the BZ. We show that (i) the viscosity coefficient is nearly proportional to B for given (V,U),and (ii) dissipation-less state, analogous to superfluidity, is possible for a critical value of U when (V, B) are given. We also calculate the entropy per particle (S) and show that the results comply with the KSS bound reported by Kovtun et al.