Crossover in the two-impurity Kondo model induced by direct charge tunneling

Quantum critical behavior in the two-impurity Kondo model requires the distinct separation of two scales, T_K >> T*, where T_K is the Kondo temperature and T* is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi liquid fixed point. We provide a derivation of T* based on the renormalization group to lowest order. This result is confirmed by a numerical renormalization group (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi liquid fixed point is derived and subsequently confirmed by the NRG. We discuss implications for series double quantum dot systems.Comment: 10 pages, 6 figures; resubmitted Oct. 31, 2011 to include corrections discovered after original submissio

The Influence of Interference on the Kondo Effect in a Quantum Dot

We study the Kondo effect in a model system of a quantum dot embedded in an Aharanov-Bohm ring connected to two leads. By transforming to the scattering basis of the direct inter-lead tunneling, we are able to describe precisely how the Kondo screening of the dot spin occurs. We calculate the Kondo temperature and zero-temperature conductance and find that both are influenced by the Aharanov-Bohm ring as well as the electron density in the leads. We also calculate the form of an additional potential scattering term that arises at low energies due to the breaking of particle-hole symmetry. Many of our results are supported by numerical analysis using the numerical renormalization group.Comment: 24 pages, 18 figure

Quantum Gravity and Inflation

Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state.Comment: 18 Pages, 2 Figures; major corrections to equations but prior results still hold, updated reference

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T_K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.Comment: 22 pages, 1 figure; reference update

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements