Conformal maps of viscous electron flow in the Gurzhi crossover

We investigate the impact of geometric constriction on viscous flow electron liquid through quantum point contacts. provide analysis electric potential distribution given setup a slit configuration and use method conformal mapping to obtain analytical results. The profile can be tested contrasted experimentally with scanning tunneling potentiometry technique. discuss intricate physics that underlies Gurzhi effect, i.e., enhancement conductivity in flow, compare results for different boundary conditions. In addition, we calculate temperature dependence momentum relaxation time as result impurity assisted quasiballistic interference effects various correlational corrections lead violation Matthiessen's rule hydrodynamic regime. caution spatially inhomogeneous profiles current crossover between Ohmic Stokes flows might also appear nonhydrodynamic limit where nonlocality plays an important role. This conclusion is corroborated by calculation dispersive weakly impure limit.