Tunable Fano-Kondo resonance in side-coupled double quantum dot system

We study the interference between the Fano and Kondo effects in a side-coupled double-quantum- dot system where one of the quantum dots couples to conduction electron bath while the other dot only side-couples to the first dot via antiferromagnetic (AF) spin exchange coupling. We apply both the perturbative renormalization group (RG) and numerical renormalization group (NRG) approaches to study the effect of AF coupling on the Fano lineshape in the conduction leads. With particle-hole symmetry, the AF exchange coupling competes with the Kondo effect and leads to a local spin-singlet ground state for arbitrary small coupling, so called "two-stage Kondo effect". As a result, via NRG we find the spectral properties of the Fano lineshape in the tunneling density of states (TDOS) of conduction electron leads shows double dip-peak features at the energy scale around the Kondo temperature and the one much below it, corresponding to the two-stage Kondo effect; it also shows an universal scaling behavior at very low energies. We find the qualitative agreement between the NRG and the perturbative RG approach. Relevance of our work to the experiments is discussed.Comment: 7 pages, 7 figure

Discovery of Counter-Rotating Gas in the Galaxies NGC1596 and NGC3203 and the Incidence of Gas Counter-Rotation in S0 Galaxies

We have identified two new galaxies with gas counter-rotation (NGC1596 and NGC3203) and have confirmed similar behaviour in another one (NGC128), this using results from separate studies of the ionized-gas and stellar kinematics of a well-defined sample of 30 edge-on disc galaxies. Gas counter-rotators thus represent 10+/-5% of our sample, but the fraction climbs to 21+/-11% when only lenticular (S0) galaxies are considered and to 27+/-13% for S0s with detected ionized-gas only. Those fractions are consistent with but slightly higher than previous studies. A compilation from well-defined studies of S0s in the literature yields fractions of 15+/-4% and 23+/-5%, respectively. Although mainly based on circumstantial evidence, we argue that the counter-rotating gas originates primarily from minor mergers and tidally-induced transfer of material from nearby objects. Assuming isotropic accretion, twice those fractions of objects must have undergone similar processes, underlining the importance of (minor) accretion for galaxy evolution. Applications of gas counter-rotators to barred galaxy dynamics are also discussed.Comment: 8 pages, including 1 table and 2 figures. Accepted for publication in MNRAS. Version with full resolution figures available at http://www-astro.physics.ox.ac.uk/~bureau/pub_list.htm

Common adversaries form alliances: modelling complex networks via anti-transitivity

Anti-transitivity captures the notion that enemies of enemies are friends, and arises naturally in the study of adversaries in social networks and in the study of conflicting nation states or organizations. We present a simplified, evolutionary model for anti-transitivity influencing link formation in complex networks, and analyze the model's network dynamics. The Iterated Local Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step, and joins anti-clones to the parent node's non-neighbor set. The graphs generated by ILAT exhibit familiar properties of complex networks such as densification, short distances (bounded by absolute constants), and bad spectral expansion. We determine the cop and domination number for graphs generated by ILAT, and finish with an analysis of their clustering coefficients. We interpret these results within the context of real-world complex networks and present open problems

Quantum criticality in a double quantum-dot system

We discuss the realization of the quantum-critical non-Fermi liquid state, originally discovered within the two-impurity Kondo model, in double quantum-dot systems. Contrary to the common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries, and is only unstable to charge transfer between the two dots. We propose an experimental set-up where such charge transfer processes are suppressed, allowing a controlled approach to the quantum critical state. We also discuss transport and scaling properties in the vicinity of the critical point.Comment: 4 pages, 3 figs; (v2) final version as publishe

Quantum criticality out of equilibrium in the pseudogap Kondo model

We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels {\mu}_L/R, {\rho}_c,L(R) ({\omega}) \propto |{\omega} - {\mu}_L(R) |r, and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.Comment: 4.1 pages, 2 figure

Minimal Theoretical Uncertainties in Inflationary Predictions

During inflation, primordial energy density fluctuations are created from approximate de Sitter vacuum quantum fluctuations redshifted out of the horizon after which they are frozen as perturbations in the background curvature. In this paper we demonstrate that there exists an intrinsic theoretical uncertainty in the inflationary predictions for the curvature perturbations due to the failure of the well known prescriptions to specify the vacuum uniquely. Specifically, we show that the two often used prescriptions for defining the initial vacuum state -- the Bunch-Davies prescription and the adiabatic vacuum prescription (even if the adiabaticity order to which the vacuum is specified is infinity) -- fail to specify the vacuum uniquely in generic inflationary spacetimes in which the total duration of inflation is finite. This conclusion holds despite the absence of any trans-Planckian effects or effective field theory cutoff related effects. We quantify the uncertainty which is applicable to slow roll inflationary scenarios as well as for general FRW spacetimes and find that the uncertainty is generically small. This uncertainty should be treated as a minimal uncertainty that underlies all curvature perturbation calculations.Comment: LaTeX file, 35 pages; some typos correcte

Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification

The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dimensional Euclidean space to create nonlinear kernels. We introduce a Layered Random Projection (LaRP) framework, where we model the linear kernels and nonlinearity separately for increased training efficiency. The proposed LaRP framework was assessed using the MNIST hand-written digits database and the COIL-100 object database, and showed notable improvement in object classification performance relative to other state-of-the-art random projection methods.Comment: 5 page

Thermalization and Quantum Correlations in Exactly Solvable Models

The generalized Gibbs ensemble introduced for describing few body correlations in exactly solvable systems following a quantum quench is related to the nonergodic way in which operators sample, in the limit of infinite time after the quench, the quantum correlations present in the initial state. The nonergodicity of the correlations is thus shown \emph{analytically} to imply the equivalence with the generalized Gibbs ensemble for quantum Ising and XX spin chains as well as for the Luttinger model the thermodynamic limit, and for a broad class of initial states and correlation functions of both local and nonlocal operators.Comment: 12 pages, 4 figures. Expanded in response to Referee criticis