Mesoscopic Capacitance Oscillations

We examine oscillations as a function of Fermi energy in the capacitance of a mesoscopic cavity connected via a single quantum channel to a metallic contact and capacitively coupled to a back gate. The oscillations depend on the distribution of single levels in the cavity, the interaction strength and the transmission probability through the quantum channel. We use a Hartree-Fock approach to exclude self-interaction. The sample specific capacitance oscillations are in marked contrast to the charge relaxation resistance, which together with the capacitance defines the RC-time, and which for spin polarized electrons is quantized at half a resistance quantum. Both the capacitance oscillations and the quantized charge relaxation resistance are seen in a strikingly clear manner in a recent experiment.Comment: 9 pages, 2 figure

Gap theory of rectification in ballistic three-terminal conductors

We introduce a model for rectification in three-terminal ballistic conductors, where the central connecting node is modeled as a chaotic cavity. For bias voltages comparable to the Fermi energy, a strong nonlinearity is created by the opening of a gap in the transport window. Both noninteracting cavity electrons at arbitrary temperature as well as the hot electron regime are considered. Charging effects are treated within the transmission formalism using a self-consistent analysis. The conductance of the third lead in a voltage probe configuration is varied to also model inelastic effects. We find that the basic transport features are insensitive to all of these changes, indicating that the nonlinearity is robust and well suited to applications such as current rectification in ballistic systems. Our findings are in broad agreement with several recent experiments.Comment: 8 pages, 6 figure

New Insights into Cosmic Ray induced Biosignature Chemistry in Earth-like Atmospheres

With the recent discoveries of terrestrial planets around active M-dwarfs, destruction processes masking the possible presence of life are receiving increased attention in the exoplanet community. We investigate potential biosignatures of planets having Earth-like (N$_2$-O$_2$) atmospheres orbiting in the habitable zone of the M-dwarf star AD Leo. These are bombarded by high energetic particles which can create showers of secondary particles at the surface. We apply our cloud-free 1D climate-chemistry model to study the influence of key particle shower parameters and chemical efficiencies of NOx and HOx production from cosmic rays. We determine the effect of stellar radiation and cosmic rays upon atmospheric composition, temperature, and spectral appearance. Despite strong stratospheric O$_3$ destruction by cosmic rays, smog O$_3$ can significantly build up in the lower atmosphere of our modeled planet around AD Leo related to low stellar UVB. N$_2$O abundances decrease with increasing flaring energies but a sink reaction for N$_2$O with excited oxygen becomes weaker, stabilizing its abundance. CH$_4$ is removed mainly by Cl in the upper atmosphere for strong flaring cases and not via hydroxyl as is otherwise usually the case. Cosmic rays weaken the role of CH$_4$ in heating the middle atmosphere so that H$_2$O absorption becomes more important. We additionally underline the importance of HNO$_3$ as a possible marker for strong stellar particle showers. In a nutshell, uncertainty in NOx and HOx production from cosmic rays significantly influences biosignature abundances and spectral appearance.Comment: Manuscript version after addressing all referee comments. Published in Ap

Nonlocality of cluster states of qubits

We investigate cluster states of qubits with respect to their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a new Bell inequality that is maximally violated by the 4-qubit cluster state and is not violated by the 4-qubit GHZ state.Comment: 5 pages; paragraph V.B contains a comparison with Guehne et al., quant-ph/041005

Fireballs Loading and the Blast Wave Model of Gamma Ray Bursts

A simple function for the spectral power $P(\epsilon,t) \equiv \nu L(\nu)$ is proposed to model, with 9 parameters, the spectral and temporal evolution of the observed nonthermal synchrotron power flux from GRBs in the blast wave model. Here $\epsilon = h\nu/$m$_e$c$^2$ is the observed dimensionless photon energy and $t$ is the observing time. Assumptions and an issue of lack of self-consistency are spelled out. The spectra are found to be most sensitive to the baryon loading, expressed in terms of the initial bulk Lorentz factor $\Gamma_0$, and an equipartition term $q$ which is assumed to be constant in time and independent of $\Gamma_0$. Expressions are given for the peak spectral power $P_p(t) = P(\epsilon_p,t)$ at the photon energy $\epsilon = \epsilon_p(t)$ of the spectral power peak. A general rule is that the total fireball particle kinetic energy $E_0 \sim \Pi_0 t_d$, where $t_d \propto \Gamma_0^{-8/3}$ is the deceleration time scale and $\Pi_0 \equiv P(\epsilon_p,t_d) \propto \Gamma_0^{8/3}$ is the maximum measured bolometric power output in radiation, during which it is carried primarily by photons with energy ${\cal E}_0 = \epsilon_p(t_d) \propto q\Gamma_0^4$.Comment: 26 pages, including 4 figures, uses epsf.sty, rotate.sty; submitted to ApJ; revised version with extended introduction, redrawn figures, and correction

Theory and simulations of rigid polyelectrolytes

We present theoretical and numerical studies on stiff, linear polyelectrolytes within the framework of the cell model. We first review analytical results obtained on a mean-field Poisson-Boltzmann level, and then use molecular dynamics simulations to show, under which circumstances these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes we compute the osmotic coefficient as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. We show that this results from a reduced contribution of the virial part to the pressure. We compute the osmotic coefficient and ionic distribution functions from Poisson-Boltzmann theory with and without a recently proposed correlation correction, and also simulation results for the case of poly(para-phenylene) and compare it to recently obtained experimental data on this stiff polyelectrolyte. We also investigate ion-ion correlations in the strong coupling regime, and compare them to predictions of the recently advocated Wigner crystal theories.Comment: 32 pages, 15 figures, proceedings of the ASTATPHYS-MEX-2001, to be published in Mol. Phy

Line emission from gamma-ray burst environments

The time and angle dependent line and continuum emission from a dense torus around a cosmological gamma-ray burst source is simulated, taking into account photoionization, collisional ionization, recombination, and electron heating and cooling due to various processes. The importance of the hydrodynamical interaction between the torus and the expanding blast wave is stressed. Due to the rapid deceleration of the blast wave as it interacts with the dense torus, the material in the torus will be illuminated by a drastically different photon spectrum than observable through a low-column-density line of sight, and will be heated by the hydrodynamical interaction between the blast wave and the torus. A model calculation to reproduce the Fe K-alpha line emission observed in the X-ray afterglow of GRB 970508 is presented. The results indicate that ~ 10^{-4} solar masses of iron must be concentrated in a region of less than 10^{-3} pc. The illumination of the torus material due to the hydrodynamic interaction of the blast wave with the torus is the dominant heating and ionization mechanism leading to the formation of the iron line. These results suggest that misaligned GRBs may be detectable as X-ray flashes with pronounced iron emission line features.Comment: Accepted for publication in ApJ. Updated recombination rate data; discussion on element abundances added; references update

Upper bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles"

The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To circumvent this obstacle we introduce the notion of equivalence modulo limit cycles. This paper is the continuation of the author's paper in [Mosc. Math. J. 1 (2001), no. 4] where the lower bound of the form 2^{cn^2} has been obtained. Here we obtain the upper bound of the same form. We also associate an equipped planar graph to every planar polynomial vector field, this graph is a complete invariant for orbital topological classification of such fields.Comment: 23 pages, 5 figure

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde