Voltage probe model of spin decay in a chaotic quantum dot, with applications to spin-flip noise and entanglement production

The voltage probe model is a model of incoherent scattering in quantum transport. Here we use this model to study the effect of spin-flip scattering on electrical conduction through a quantum dot with chaotic dynamics. The spin decay rate gamma is quantified by the correlation of spin-up and spin-down current fluctuations (spin-flip noise). The resulting decoherence reduces the ability of the quantum dot to produce spin-entangled electron-hole pairs. For gamma greater than a critical value gamma_c, the entanglement production rate vanishes identically. The statistical distribution P(gamma_c) of the critical decay rate in an ensemble of chaotic quantum dots is calculated using the methods of random-matrix theory. For small gamma_c this distribution is proportional to gamma_c^(-1+beta/2), depending on the presence (beta=1) or absence (beta=2) of time-reversal symmetry. To make contact with experimental observables, we derive a one-to-one relationship between the entanglement production rate and the spin-resolved shot noise, under the assumption that the density matrix is isotropic in the spin degrees of freedom. Unlike the Bell inequality, this relationship holds for both pure and mixed states. In the tunneling regime, the electron-hole pairs are entangled if and only if the correlator of parallel spin currents is at least twice larger than the correlator of antiparallel spin currents.Comment: version 3: corrected a factor of two in Eq. (3.16), affecting the final result

Koszul Theorem for S-Lie coalgebras

For a symmetry braid S-Lie coalgebras, as a dual object to algebras introduced by Gurevich, are considered. For an Young antisymmetrizer an S-exterior algebra is introduced. From this differential point of view S-Lie coalgebras are investigated. The dual Koszul theorem in this case is proved.Comment: 8 pages, AMSLaTe

Counting statistics of coherent population trapping in quantum dots

Destructive interference of single-electron tunneling between three quantum dots can trap an electron in a coherent superposition of charge on two of the dots. Coupling to external charges causes decoherence of this superposition, and in the presence of a large bias voltage each decoherence event transfers a certain number of electrons through the device. We calculate the counting statistics of the transferred charges, finding a crossover from sub-Poissonian to super-Poissonian statistics with increasing ratio of tunnel and decoherence rates.Comment: 4 pages, 2 figure

Tidal controls on trace gas dynamics in a seagrass meadow of the Ria Formosa lagoon (southern Portugal)

Coastal zones are important source regions for a variety of trace gases, including halocarbons and sulfur-bearing species. While salt marshes, macroalgae and phyto-plankton communities have been intensively studied, little is known about trace gas fluxes in seagrass meadows. Here we report results of a newly developed dynamic flux chamber system that can be deployed in intertidal areas over full tidal cycles allowing for highly time-resolved measurements. The fluxes of CO2, methane (CH4) and a range of volatile organic compounds (VOCs) showed a complex dynamic mediated by tide and light. In contrast to most previous studies, our data indicate significantly enhanced fluxes during tidal immersion relative to periods of air exposure. Short emission peaks occurred with onset of the feeder current at the sampling site. We suggest an overall strong effect of advective transport processes to explain the elevated fluxes during tidal immersion. Many emission estimates from tidally influenced coastal areas still rely on measurements carried out during low tide only. Hence, our results may have significant implications for budgeting trace gases in coastal areas. This dynamic flux chamber system provides intensive time series data of community respiration (at night) and net community production (during the day) of shallow coastal systems.German Federal Ministry of Education and Research (BMBF) [03F0611E, 03F0662E]; EU FP7 ASSEMBLE research infrastructure initiative

Dynamics of gene expression and the regulatory inference problem

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl

Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical features of the model, namely fragmentation and multistability, we present a characterization of the temporal (periodic and chaotic) fluctuations of the quasi-stasis asymptotic states of network activity. The double (both structural and dynamical) source of entangled complexity of the system temporal fluctuations, as an important partial aspect of the Correlation Structure-Function problem, is further discussed to the light of the numerical results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major revision and new results incorporated. To appear in Chaos (2006

Quasiparticle Chirality in Epitaxial Graphene Probed at the Nanometer Scale

Graphene exhibits unconventional two-dimensional electronic properties resulting from the symmetry of its quasiparticles, which leads to the concepts of pseudospin and electronic chirality. Here we report that scanning tunneling microscopy can be used to probe these unique symmetry properties at the nanometer scale. They are reflected in the quantum interference pattern resulting from elastic scattering off impurities, and they can be directly read from its fast Fourier transform. Our data, complemented by theoretical calculations, demonstrate that the pseudospin and the electronic chirality in epitaxial graphene on SiC(0001) correspond to the ones predicted for ideal graphene.Comment: 4 pages, 3 figures, minor change

Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group

A local classification of all Poisson-Lie structures on an infinite-dimensional group $G_{\infty}$ of formal power series is given. All Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of $G_{\infty}$ are also classified.Comment: 11 pages, AmSTeX fil

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering