Capacitance, admittance, and rectification properties of small conductors

We formulate microscopic expressions for capacitances, admittances and the rectification properties for small phase-coherent samples consisting of a number of metallic layers separated by insulators. The electric potential in such a structure is discussed with the help of characteristic functions which determine the variation of the microscopic potential inside the sample in response to an increase of the electro-chemical potential at a contact. An electrochemical capacitance matrix is derived which allows for field penetration into the conductor. We discuss the admittance matrix for conductors with nearby capacitors (gates) and analyse its magnetic field symmetry. We use the characteristic potentials to discuss the rectification properties of a conduction channel in the presence of nearby capacitors.