The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the experimentally observed width and shift of the Kondo resonance are in accordance with those obtained from a combination of band structure and strongly correlated calculations.

We consider electron transport through a quantum dot described by the Kondo model in the regime of large transport voltage $V$ in the presence of a magnetic field $B$ with $\max (V,B)\gg T_K$. The electric current $I$ and the local magnetization $M$ are found to be universal functions of $V/T_K$ and $B/T_K$, where $T_K$ is the equilibrium Kondo temperature. We present a generalization of the perturbative renormalization group to frequency dependent coupling functions, as necessitated by the structure of bare perturbation theory. We calculate $I$ and $M$ within a poor man’s scaling approach and find excellent agreement with experiment.

We examine the properties of a dc-biased quantum dot in the Coulomb blockade regime. For voltages $V$ that are large compared to the Kondo temperature $T_K$, the physics is governed by the scales $V$ and $\gamma$, where $\gamma \sim V/{ln}^2\left({V/T}_K\right)$ is the nonequilibrium decoherence rate induced by the voltage-driven current. Based on scaling arguments, self-consistent perturbation theory, and perturbative renormalization group, we argue that due to the large $\gamma$ the system can be described by renormalized perturbation theory in $1/\ln \left({V/T}_K\right)\ll 1$. However, in certain variants of the Kondo problem, two-channel Kondo physics is induced by a large voltage $V$.

We study the Kondo effect generated by a single magnetic impurity embedded in an ultrasmall metallic grain, to be called a “Kondo box.” We find that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature, in a way that depends on the parity of the number of electrons on the grain. We show that the single-electron tunneling conductance through such a grain features Kondo-induced Fano-type resonances of measurable size, with an anomalous dependence on temperature and level spacing.

A dissipative quantum gas of light: Our textbook understanding of quantum systems tends to come from modeling these systems isolated from the environment. However, an emerging focus is understanding how many-body quantum systems behave when interacting with their surroundings and how they subsequently become dissipative, or non-Hermitian, systems. Öztürk et al. formed a quantum condensate of light by trapping photons in an optical cavity, a system that is naturally dissipative. By altering the trapping conditions, they demonstrated that the system provides a powerful platform with which to explore the complex dynamics and phase transitions occurring in dissipative quantum systems. Science , this issue p. 88

We present an extension of the noncrossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $\overrightarrow{U}\infty ,$ to the case of finite U. A self-consistent conserving pseudoparticle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the “symmetrized finite-$U$ NCA” (SUNCA). We show that within SUNCA the low-energy scale $T_K$ (Kondo temperature) is correctly obtained, in contrast to other simpler approximations discussed in the literature.