Universal zero-bias conductance through a quantum wire side-coupled to a quantum dot

A numerical renormalization-group study of the conductance through a quantum wire side-coupled to a quantum dot is reported. The temperature and the dot-energy dependence of the conductance are examined in the light of a recently derived linear mapping between the Kondo-regime temperature-dependent conductance and the universal function describing the conductance for the symmetric Anderson model of a quantum wire with an embedded quantum dot. Two conduction paths, one traversing the wire, the other a bypass through the quantum dot, are identified. A gate potential applied to the quantum wire is shown to control the flow through the bypass. When the potential favors transport through the wire, the conductance in the Kondo regime rises from nearly zero at low temperatures to nearly ballistic at high temperatures. When it favors the dot, the pattern is reversed: the conductance decays from nearly ballistic to nearly zero. When the fluxes through the two paths are comparable, the conductance is nearly temperature-independent in the Kondo regime, and a Fano antiresonance in the fixed-temperature plot of the conductance as a function of the dot energy signals interference. Throughout the Kondo regime and, at low temperatures, even in the mixed-valence regime, the numerical data are in excellent agreement with the universal mapping.Comment: 12 pages, with 9 figures. Submitted to PR

Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ

General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.Comment: 4 pages. Comment to Class. Quantum Grav. 18(2001)L8

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering from this instability decrease to around 100Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000

r-modes in Relativistic Superfluid Stars

We discuss the modal properties of the $r$-modes of relativistic superfluid neutron stars, taking account of the entrainment effects between superfluids. In this paper, the neutron stars are assumed to be filled with neutron and proton superfluids and the strength of the entrainment effects between the superfluids are represented by a single parameter $\eta$. We find that the basic properties of the $r$-modes in a relativistic superfluid star are very similar to those found for a Newtonian superfluid star. The $r$-modes of a relativistic superfluid star are split into two families, ordinary fluid-like $r$-modes ($r^o$-mode) and superfluid-like $r$-modes ($r^s$-mode). The two superfluids counter-move for the $r^s$-modes, while they co-move for the $r^o$-modes. For the $r^o$-modes, the quantity $\kappa\equiv\sigma/\Omega+m$ is almost independent of the entrainment parameter $\eta$, where $m$ and $\sigma$ are the azimuthal wave number and the oscillation frequency observed by an inertial observer at spatial infinity, respectively. For the $r^s$-modes, on the other hand, $\kappa$ almost linearly increases with increasing $\eta$. It is also found that the radiation driven instability due to the $r^s$-modes is much weaker than that of the $r^o$-modes because the matter current associated with the axial parity perturbations almost completely vanishes.Comment: 14 pages, 4 figures. To appear in Physical Review

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\bar\sigma$ of the fundamental $r$-mode is in a good approximation given by $\bar\sigma\approx \kappa_0 \Omega$, where $\bar\sigma$ is defined in the corotating frame at the spatial infinity, and $\Omega$ is the angular frequency of rotation of the star. The proportional coefficient $\kappa_0$ is only weakly dependent on $\Omega$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $\Omega$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.Comment: 22 pages, 8 figures, accepted for publication in Ap

Thermal dependence of the zero-bias conductance through a nanostructure

We show that the conductance of a quantum wire side-coupled to a quantum dot, with a gate potential favoring the formation of a dot magnetic moment, is a universal function of the temperature. Universality prevails even if the currents through the dot and the wire interfere. We apply this result to the experimental data of Sato et al.[Phys. Rev. Lett. 95, 066801 (2005)].Comment: 6 pages, 3 figures. More detailed presentation, and updated references. Final version