History dependence, memory and metastability in electron glasses

We discuss the history dependence and memory effects which are observed in the out-of-equilibrium conductivity of electron glasses. The experiments can be understood by assuming that the local density of states retains a memory of the sample history. We provide analytical arguments for the consistency of this assumption, and discuss the saturation of the memory effect with increasing gate voltage change. This picture is bolstered by numerical simulations at zero temperature, which moreover demonstrate the incompressibility of the Coulomb glass on short timescales.Comment: 4 pages, 1 figur

Statistical and Computational Tradeoffs in Stochastic Composite Likelihood

Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of the estimators resolve the computation-accuracy tradeoff differently, and taken together they span a continuous spectrum of computation-accuracy tradeoff resolutions. We prove the consistency of the estimators, provide formulas for their asymptotic variance, statistical robustness, and computational complexity. We discuss experimental results in the context of Boltzmann machines and conditional random fields. The theoretical and experimental studies demonstrate the effectiveness of the estimators when the computational resources are insufficient. They also demonstrate that in some cases reduced computational complexity is associated with robustness thereby increasing statistical accuracy.Comment: 30 pages, 97 figures, 2 author

Non-equilibrium conductance of a three-terminal quantum dot in the Kondo regime: Perturbative Renormalization Group

Motivated by recent experiments, we consider a single-electron transistor in the Kondo regime which is coupled to three leads in the presence of large bias voltages. Such a steady-state non-equilibrium system is to a large extent governed by a decoherence rate induced by the current through the dot. As the two-terminal conductance turns out to be rather insensitive to the decoherence rate, we study the conductance in a three-terminal device using perturbative renormalization group and calculate the characteristic splitting of the Kondo resonance. The interplay between potential biases and anisotropy in coupling to the three leads determines the decoherence rate and the conditions for strong coupling.Comment: 4 pages, 4 figure