Adiabatic Dynamics of Superconducting Quantum Point Contacts

摘要

Starting from the quasiclassical equations for non-equilibrium Green'sfunctions we derive a simple kinetic equation that governs ac Josephson effectin a superconducting quantum point contact at small bias voltages. In contrastto existing approaches the kinetic equation is valid for voltages witharbitrary time dependence. We use this equation to calculatefrequency-dependent linear conductance, and dc $I\!-\!V$ characteristics withand without microwave radiation for resistively shunted quantum point contacts.A novel feature of the $I\!-\!V$ characteristics is the excess current$2I_c/\pi$ appearing at small voltages. An important by-product of ourderivation is the analytical proof that the microscopic expression for thecurrent coincides at arbitrary voltages with the expression that follows fromthe Bogolyubov-de Gennes equations, if one uses appropriate amplitudes ofAndreev reflection which contain information about microscopic structure of thesuperconductors.