Stochastic properties of systems controlled by autocatalytic reactions II

We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X, X+X -> A+X, X -> B provided that the distribution of reacting particles in the system volume is uniform, i.e. the point model of reaction kinetics introduced in arXiv:cond-mat/0404402 can be applied. Assuming the number of substrate particles A to be kept constant by a suitable reservoir, we derived the forward Kolmogorov equation for the probability of finding n=0,1,... autocatalytic particles X in the system at a given time moment. We have shown that the stochastic model results in an equation for the mean value of autocatalytic particles X which differs strongly from the kinetic rate equation. It has been found that not only the law of the mass action is violated but also the bifurcation point is disappeared in the well-known diagram of X particle- vs. A particle-concentration. Therefore, speculations about the role of autocatalytic reactions in processes of the "natural selection" can be hardly supported.Comment: 17 pages, 6 figure

η\eta-meson in nuclear matter

The $\eta$-nucleon ($\eta$N) interactions are deduced from the heavy baryon chiral perturbation theory up to the next-to-leading-order terms. Combining the relativistic mean-field theory for nucleon system, we have studied the in-medium properties of $\eta$-meson. We find that all the elastic scattering $\eta$N interactions come from the next-to-leading-order terms. The $\eta$N sigma term is found to be about 280$\pm$130 MeV. The off-shell terms are also important to the in-medium properties of $\eta$-meson. On application of the latest determination of the $\eta$N scattering length, the ratio of $\eta$-meson effective mass to its vacuum value is near $0.84\pm0.015$, while the optical potential is about $-(83\pm5)$ MeV, at the normal nuclear density.Comment: 8 pages, 3 figures, to appear in PRC, many modification

LICOR-Liquid Columns' Resonances

The aim of the experiment LICOR was the investigation of the axial resonances oi cylindrical liquid columns supported by equal circular coaxiaJ disks. In preparation ot the D-2 experiment a •heoreiical model has been developed, which exactly describes the small amplitude oscillations of finite cylindrical columns between coaxial circular disks. In addition, in terrestrial experiments the resonance frequencies of small liquid columns with up to 5 mm in diameter have been determined and investigations with density-matched liquids (silicon oil in a waierlmethanol mixture) have been performed. For the D-2 experiment LICOR the front disk and the rear disk lor use in the AFPM have been constructed and equipped with pressure sensors and the necessary electronics. The pressure exerted by the oscillating liquid column on trie supporting disks vsas as low as 10 Pa. Since the data downlink of the Materials Research Laboratory was just one signal oer second and channel, it was necessary to determine amplitude and phase of the pressure already in the LICOR disks. The D-2 experiment has been successfully performed. It has fully confirmed the theoretical models and remarkably supplements the experiments on small liquid columns and on density-matched columns

Microcavity controlled coupling of excitonic qubits

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. The most relevant mechanism of coherent coupling of distant qubits is coupling via the electromagnetic field. Here, we demonstrate the controlled coherent coupling of spatially separated excitonic qubits via the photon mode of a solid state microresonator. This is revealed by two-dimensional spectroscopy of the sample's coherent response, a sensitive and selective probe of the coherent coupling. The experimental results are quantitatively described by a rigorous theory of the cavity mediated coupling within a cluster of quantum dots excitons. Having demonstrated this mechanism, it can be used in extended coupling channels - sculptured, for instance, in photonic crystal cavities - to enable a long-range, non-local wiring up of individual emitters in solids

Physical Adsorption at the Nanoscale: Towards Controllable Scaling of the Substrate-Adsorbate van der Waals Interaction

The Lifshitz-Zaremba-Kohn (LZK) theory is commonly considered as the correct large-distance limit for the van der Waals (vdW) interaction of adsorbates (atoms, molecules, or nanoparticles) with solid substrates. In the standard approximate form, implicitly based on "local" dielectric functions, the LZK approach predicts universal power laws for vdW interactions depending only on the dimensionality of the interacting objects. However, recent experimental findings are challenging the universality of this theoretical approach at finite distances of relevance for nanoscale assembly. Here, we present a combined analytical and numerical many-body study demonstrating that physical adsorption can be significantly enhanced at the nanoscale. Regardless of the band gap or the nature of the adsorbate specie, we find deviations from conventional LZK power laws that extend to separation distances of up to 10--20 nanometers. Comparison with recent experimental observation of ultra long-ranged vdW interactions in the delamination of graphene from a silicon substrate reveals qualitative agreement with the present theory. The sensitivity of vdW interactions to the substrate response and to the adsorbate characteristic excitation frequency also suggests that adsorption strength can be effectively tuned in experiments, paving the way to an improved control of physical adsorption at the nanoscale

Impact of phonons on dephasing of individual excitons in deterministic quantum dot microlenses

Optimized light-matter coupling in semiconductor nanostructures is a key to understand their optical properties and can be enabled by advanced fabrication techniques. Using in-situ electron beam lithography combined with a low-temperature cathodoluminescence imaging, we deterministically fabricate microlenses above selected InAs quantum dots (QDs) achieving their efficient coupling to the external light field. This enables to perform four-wave mixing micro-spectroscopy of single QD excitons, revealing the exciton population and coherence dynamics. We infer the temperature dependence of the dephasing in order to address the impact of phonons on the decoherence of confined excitons. The loss of the coherence over the first picoseconds is associated with the emission of a phonon wave packet, also governing the phonon background in photoluminescence (PL) spectra. Using theory based on the independent boson model, we consistently explain the initial coherence decay, the zero-phonon line fraction, and the lineshape of the phonon-assisted PL using realistic quantum dot geometries

Retardation turns the van der Waals attraction into Casimir repulsion already at 3 nm

Casimir forces between surfaces immersed in bromobenzene have recently been measured by Munday et al. Attractive Casimir forces were found between gold surfaces. The forces were repulsive between gold and silica surfaces. We show the repulsion is due to retardation effects. The van der Waals interaction is attractive at all separations. The retardation driven repulsion sets in already at around 3 nm. To our knowledge retardation effects have never been found at such a small distance before. Retardation effects are usually associated with large distances

Excitons in T-shaped quantum wires

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/Al$_{x}$Ga$_{1-x}$As and In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction $x$. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/Al$_{x}$Ga$_{1-x}$As wires we obtain an upper limit for the binding energy of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical Review