Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order

The master equation describing the non-equilibrium dynamics of a quantum dot coupled to metallic leads is considered. Employing a superoperator approach, we derive an exact time-convolutionless master equation for the probabilities of dot states, i.e., a time-convolutionless Pauli master equation. The generator of this master equation is derived order by order in the hybridization between dot and leads. Although the generator turns out to be closely related to the T-matrix expressions for the transition rates, which are plagued by divergences, in the time-convolutionless generator all divergences cancel order by order. The time-convolutionless and T-matrix master equations are contrasted to the Nakajima-Zwanzig version. The absence of divergences in the Nakajima-Zwanzig master equation due to the nonexistence of secular reducible contributions becomes rather transparent in our approach, which explicitly projects out these contributions. We also show that the time-convolutionless generator contains the generator of the Nakajima-Zwanzig master equation in the Markov approximation plus corrections, which we make explicit. Furthermore, it is shown that the stationary solutions of the time-convolutionless and the Nakajima-Zwanzig master equations are identical. However, this identity neither extends to perturbative expansions truncated at finite order nor to dynamical solutions. We discuss the conditions under which the Nakajima-Zwanzig-Markov master equation nevertheless yields good results.Comment: 13 pages + appendice

Doping dependence of the Neel temperature in Mott-Hubbard antiferromagnets: Effect of vortices

The rapid destruction of long-range antiferromagnetic order upon doping of Mott-Hubbard antiferromagnetic insulators is studied within a generalized Berezinskii-Kosterlitz-Thouless renormalization group theory in accordance with recent calculations suggesting that holes dress with vortices. We calculate the doping-dependent Neel temperature in good agreement with experiments for high-Tc cuprates. Interestingly, the critical doping where long-range order vanishes at zero temperature is predicted to be xc ~ 0.02, independently of any energy scales of the system.Comment: 4 pages with 3 figures included, minor revisions, to be published in PR

Nomadic Behavior of an Old and Formerly Territorial Eastern Coyote, Canis latrans

We document the fate of a female Eastern Coyote on Cape Cod, Massachusetts that was a breeding resident of a ~30 km2 territory for at least six years (1998 – 2004) and then became nomadic. Her behavior dramatically changed in January 2005, when she was located on six occasions sleeping under sheds and/or decks in highly residential neighborhoods at the southeastern edge of her range. On 11 March 2005 she localized in a small area (95% MCP range = 5.85 km2) at the northeastern edge of her old territory, where she remained until 1 March 2006. After briefly associating with other Coyotes (late-February 2006), her movement patterns changed again. She used a much larger area (~200 km2) until she was shot dead in February 2007. Tracking data indicated that she lived in localized areas during this nomadic period, possibly to avoid resident Coyote packs

Clustering in disordered ferromagnets: The Curie temperature in diluted magnetic semiconductors

We theoretically investigate impurity correlation and magnetic clustering effects on the long-range ferromagnetic ordering in diluted magnetic semiconductors, such as $\textrm{Ga}_{1-x}\textrm{Mn}_{x}\textrm{As}$, using analytical arguments and direct Monte Carlo simulations. We obtain an analytic formula for the ferromagnetic transition temperature $T_{c}$ which becomes asymptotically exact in the strongly disordered, highly dilute (i.e. small $x$) regime. We establish that impurity correlations have only small effects on $T_{c}$ with the neutrally correlated random disorder producing the nominally highest $T_{c}$. We find that the ferromagnetic order is approached from the high temperature paramagnetic side through a random magnetic clustering phenomenon consistent with the percolation transition scenario.Comment: 5 pages, 4 figure

Liquid antiferromagnets in two dimensions

It is shown that, for proper symmetry of the parent lattice, antiferromagnetic order can survive in two-dimensional liquid crystals and even isotropic liquids of point-like particles, in contradiction to what common sense might suggest. We discuss the requirements for antiferromagnetic order in the absence of translational and/or orientational lattice order. One example is the honeycomb lattice, which upon melting can form a liquid crystal with quasi-long-range orientational and antiferromagnetic order but short-range translational order. The critical properties of such systems are discussed. Finally, we draw conjectures for the three-dimensional case.Comment: 4 pages RevTeX, 4 figures include

Coywolf, Canis latrans × lycaon, Pack Density Doubles Following the Death of a Resident Territorial Male

We studied a subset of four radio-collared individuals that were a part of a larger study documenting Coywolf (Canis latrans × lycaon; Eastern Coyote) ecology in an urbanized landscape (Cape Cod, Massachusetts), and report on the territory of a typical sized pack that was subdivided roughly in half following the death of the breeding male from the original ("Centerville") pack. The original residents lived in a winter pack size (i.e., after pup/juvenile dispersal) of three or four individuals in a 19.66 km2 territory and a density of 0.15-0.20 individuals/km2, as determined by radio-tracking and direct observations, with their territory bordering that of other monitored packs. Following the death of the breeding male, two other radio-collared Coywolves (a young male from the original Centerville pack and a young female from a bordering pack) shifted their respective territories to overlap the majority of the original Centerville pack's territory. These two groups were the same size as the original pack (three or four individuals each) but occupied smaller territories (5.28 km2 and 12.70 km2) within the previous pack's territory. The combined density for the two new packs was estimated at 0.33-0.45 individuals/km2 or 2.2 times greater than the former pack's density and was 2.5 times (0.38-0.50 individuals/km2) greater when accounting for the slight (12%) overlap between the territories of the two new packs. Our results suggest that local Coyote/Coywolf density (i.e., at the pack level) may increase following the death of the breeding male of a given pack, probably because of the reduced (or lack of) protection of territorial boundaries. This finding has particular relevance to Coyote/Coywolf management programs aimed at reducing local densities via removal of individuals from these populations. Further implications exist for enriching our understanding of the trophic dynamics of urbanized habitats

Resonant and Kondo tunneling through molecular magnets

Transport through molecular magnets is studied in the regime of strong coupling to the leads. We consider a resonant-tunneling model where the electron spin in a quantum dot or molecule is coupled to an additional local, anisotropic spin via exchange interaction. The two opposite regimes dominated by resonant tunneling and by Kondo transport, respectively, are considered. In the resonant-tunneling regime, the stationary state of the impurity spin is calculated for arbitrarily strong molecule-lead coupling using a master-equation approach, which treats the exchange interaction perturbatively. We find that the characteristic fine structure in the differential conductance persists even if the hybridization energy exceeds thermal energies. Transport in the Kondo regime is studied within a diagrammatic approach. We show that magnetic anisotropy gives rise to a splitting of the Kondo peak at low bias voltages.Comment: 13 pages, 5 figures, version as publishe

Magnetic susceptibilities of diluted magnetic semiconductors and anomalous Hall-voltage noise

The carrier spin and impurity spin densities in diluted magnetic semiconductors are considered using a semiclassical approach. Equations of motions for the spin densities and the carrier spin current density in the paramagnetic phase are derived, exhibiting their coupled diffusive dynamics. The dynamical spin susceptibilities are obtained from these equations. The theory holds for p-type and n-type semiconductors doped with magnetic ions of arbitrary spin quantum number. Spin-orbit coupling in the valence band is shown to lead to anisotropic spin diffusion and to a suppression of the Curie temperature in p-type materials. As an application we derive the Hall-voltage noise in the paramagnetic phase. This quantity is critically enhanced close to the Curie temperature due to the contribution from the anomalous Hall effect.Comment: 18 pages, 1 figure include