Overdamped quantum phase diffusion and charging effects in Josephson junctions

Exploiting the recently derived quantum Smoluchowski equation the classical Ivanchenko Zil'berman theory for overdamped diffusive phase motion of low capacitance Josephson junctions is extended to the low temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb blockade physics, coherent Cooper pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.Comment: 10 pages, 3 figures, revised version, to appear in EuroPhys. Let

Linear dynamics subject to thermal fluctuations and non-Gaussian noise: From classical to quantum

The dynamics of a linear system embedded in a heat bath environment and subject to non- Gaussian noise is studied. Higher order cumulants in coordinate space are derived and their impact on the dynamics and on asymptotic steady state distributions is analyzed. In the quantum regime non-Gaussian properties are present in the reduced density in coordinate representation which in energy representation exist on a transient time scale only due to symmetry. Within an exactly solvable model our results provide insight into mechanisms of linear detectors as sensors for non- Gaussian noise at high and low temperatures.Comment: 7 pages, 2 figure

The partition function of an interacting many body system: beyond the perturbed static path approximation

Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures. Thereby, special attention must be paid to instabilities of the classical mean field solution in functional space that cause divergencies within the conventional PSPA. As a result we develop an approximation applicable from high to very low temperatures. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin model. In particular, we obtain a very good approximation to the level density of the Lipkin model even at low thermal excitations. Our results may have potential applications in low temperature nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. PACS: 5.30.-d, 24.60.-k, 21.10.Ma, 74.25.BtComment: 11 pages, 7 figures, replaced with shortened version accepted for publication in EPJB, minor changes not affecting any result

Low-temperature quantum fluctuations in overdamped ratchets

At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived. As a non-trivial situation to reveal the impact of subleading quantum corrections and to demonstrate convergence properties of the perturbation series, directed transport in ratchets is studied. It is shown that the perturbation series typically has a non-monotonous behavior. Depending on symmetry properties higher order contributions may even compensate current reversals induced by leading quantum fluctuations. This analysis demonstrates how to consistently treat the dynamics of overdamped quantum systems at low temperatures also in numerical applications.Comment: 5 pages, 3 figure

Low temperature electron transfer in strongly condensed phase

Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix of the electronic+reaction coordinate compound in terms of path integrals, recent findings on the overdamped limit in quantum dissipative systems are employed. This allows to give for the first time a consistent generalization of the well-known Zusman equations to the quantum domain. Detailed conditions for the range of validity are specified. Using the Wigner transform these results are also extended to the quantum dynamics in full phase space. As an important application electronic transfer rates are derived that comprise adiabatic and nonadiabatic processes in the low temperature regime including nuclear tunneling. Accurate agreement with precise quantum Monte Carlo data is observed.Comment: 16 pages, 6 figures, revised version with minor change