The current-voltage characteristic of an ultrasmall tunnel junction is calculated for arbitrary frequency dependence of the impedance presented to the junction by its electromagnetic environment. It is shown that the Coulomb blockade of tunneling is washed out by quantum fluctuations of the charge on the junction capacitor except for ultrahigh impedance environments. Two simple cases where the environment can be treated as an inductor or resistor are examined in detail. Effects of finite temperatures are discussed.

With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.

A theoretical analysis is presented of the problem of the onset of global phase coherence in granular superconductors and Josephson-junction arrays. It is shown that the ratio $\frac{\left(\frac{h}{e^2}\right)}{R}$, where $R$ is the resistance, plays an important role in the thermodynamics. This is due to quantum fluctuations of the order parameter and occurs in superconductivity only because the phase of the order parameter is both a statistical as well as a dynamical variable. The theory provides a natural qualitative explanation of the recent experiments of Orr, Jaeger, Goldman, and Kuper.

The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an LC transmission line of finite length is discussed.