Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.An electrical current induced in a resistive circuit will rapidly decay in the absence of an applied voltage. This decay reflects the tendency of the circuit's electrons to dissipate energy and relax to their ground state. However quantum mechanics predicts that the electrons' many-body ground state (and, at finite temperature, their thermal equilibrium state) may itself contain a "persistent" current which flows through the resistive circuit without dissipating energy or decaying. A dissipationless equilibrium current flowing through a resistive circuit is highly counterintuitive, but it has a familiar analog in atomic physics: some atomic species' electronic ground states possess non-zero orbital angular momentum, equivalent to a current circulating around the atom.Theoretical treatments of persistent currents (PC) in resistive metal rings have been developed over a number of decades (see [1,2] and references therein). Calculations which take 1

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An exact expression for the exchange and correlation energy of an inhomogeneous electron gas, as defined by Hohenberg, Kohn and Sham, is derived. This expression is separated into exchange and correlation terms and a formula linking the surface exchange energy of a half space to the Kohn-Sham one electron potential follows without approximation. For an infinite barrier model, the local density (Slater) approximation gives a surface exchange energy 50% greater than the exact value, a large and previously unsuspected error. An exact evaluation of the surface correlation energy is not feasible, but we argue that the dominant contribution, srising from the difference in zero point energy between bounded and unbounded systems, can beestimated using a simple model. Numerical results, not dependent on the introduction of arbitrary plasmon wavevector cutoffs, give surface correlation energies larger than Lang and Kohn (LK), who work from a local formula, by a factor of six. We discuss the consequences of our work for the agreement with experimental surface energies achieved by LK.

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