Capacitance, entanglement energetics and persistent currents of mesoscopic rings*

Small rings are a quintessential mesoscopic system. As a consequence of quantum coherence small normal metal rings support a persistent current. Novel experimental techniques will permit to investigate rings with geometries which highlight the effects of interactions. We discuss rings with in-line and side quantum dots. In the Coulomb blockade regime we derive an effective two-state Hamiltonian and discuss the flux dependence of the Coulomb blockade peaks in the capacitance and the persistent current [1]. Different nearly degenerate charge configurations of the ring-dot system become entangled with an electrical environment. With an environment consisting of an external resistor capacitively coupled to the ring and dot the entire system maps on a spin boson problem. Analysis shows that the visibility of the persistent current decreases with increasing coupling to the environment [2]. The system-bath entanglement which is at the origin of this phenomenon can be detected by projective measurements of the energy of the ring-dot subsystem or the persistent current: even in the ground state of the total system the ring can be found with some probability in the energetically higher lying state [3]. The distribution of energy or of the persistent currents is a direct measure of the system bath entanglement. \\[4pt] [1] M. Buttiker and C. A. Stafford, Phys. Rev. Lett. 76, 495 (1996); \\[0pt] [2] P. Cedraschi, V. V. Ponomarenko, and M. Buttiker, Phys. Rev. Lett. 84, 346 (2000); P. Cedraschi and M. Buttiker, Annals of Physics, 289, 1 (2001). \\[0pt] [3] A. N. Jordan and M. Buttiker, Phys. Rev. Lett. 92, 247901 (2004); M. Buttiker and A. N. Jordan, Physica E 29, 272 (2005); K. Le Hur, Annals of Physics, 323, 2208 (2008).