Averaged cubature schemes on the real positive semiaxis

Stratified cubature rules are proposed to approximate double integrals defined on the real positive semiaxis. In particular, anti-Gauss cubature formulae are introduced and averaged cubature schemes are developed. Some of their appropriate modifications are also studied. Several numerical experiments are given to testify the performance of all the formulae

Effect of bonding of a CO molecule on the conductance of atomic metal wires

We have measured the effect of bonding of a CO molecule on the conductance of Au, Cu, Pt, and Ni atomic contacts at 4.2 K. When CO gas is admitted to the metal nano contacts, a conductance feature appears in the conductance histogram near 0.5 of the quantum unit of conductance, for all metals. For Au, the intensity of this fractional conductance feature can be tuned with the bias voltage, and it disappears at high bias voltage (above $\sim$ 200 mV). The bonding of CO to Au appears to be weakest, and associated with monotomic Au wire formation.Comment: 6 figure

Evidence for a single hydrogen molecule connected by an atomic chain

Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with H$_2$ at cryogenic temperatures it has been shown that a peak near 1 $G{_0}$ identifies a single molecule Pt-H$_{2}$-Pt bridge. The histogram shows an additional structure with lower conductance that has not been identified. Here, we show that it is likely due to a hydrogen decorated Pt chain in contact with the H$_2$ molecular bridge.Comment: 4 pages, 4 figure

Vibrationally Induced Two-Level Systems in Single-Molecule Junctions

Single-molecule junctions are found to show anomalous spikes in dI/dV spectra. The position in energy of the spikes are related to local vibration mode energies. A model of vibrationally induced two-level systems reproduces the data very well. This mechanism is expected to be quite general for single-molecule junctions. It acts as an intrinsic amplification mechanism for local vibration mode features and may be exploited as a new spectroscopic tool.Comment: 4 pages, 4 figure

Stretching dependence of the vibration modes of a single-molecule Pt-H2-Pt bridge

A conducting bridge of a single hydrogen molecule between Pt electrodes is formed in a break junction experiment. It has a conductance near the quantum unit, G_0 = 2e^2/h, carried by a single channel. Using point contact spectroscopy three vibration modes are observed and their variation upon stretching and isotope substitution is obtained. The interpretation of the experiment in terms of a Pt-H_2-Pt bridge is verified by Density Functional Theory calculations for the stability, vibrational modes, and conductance of the structure.Comment: 5 pages, 4 figure

The molecular signature of highly conductive metal-molecule-metal junctions

The simplicity of single-molecule junctions based on direct bonding of a small molecule between two metallic electrodes make them an ideal system for the study of fundamental questions related to molecular electronics. Here we study the conductance properties of six different molecules suspended between Pt electrodes. All the molecular junctions show a typical conductance of about 1G0 which is ascribed to the dominant role of the Pt contacts. However, despite the metallic-like conductivity, the individual molecular signature is well-expressed by the effect of molecular vibrations in the inelastic contribution to the conductance.Comment: 7 pages, 7 figures, 1 table. Related paper: J. Ferrer and V. M. Garc\'ia-Su\'arez, Phys. Rev. B 80, 085426 (2009

Shot noise suppression at room temperature in atomic-scale Au junctions

Shot noise encodes additional information not directly inferable from simple electronic transport measurements. Previous measurements in atomic-scale metal junctions at cryogenic temperatures have shown suppression of the shot noise at particular conductance values. This suppression demonstrates that transport in these structures proceeds via discrete quantum channels. Using a high frequency technique, we simultaneously acquire noise data and conductance histograms in Au junctions at room temperature and ambient conditions. We observe noise suppression at up to three conductance quanta, with possible indications of current-induced local heating and $1/f$ noise in the contact region at high biases. These measurements demonstrate the quantum character of transport at room temperature at the atomic scale. This technique provides an additional tool for studying dissipation and correlations in nanodevices.Comment: 15 pages, 4 figures + supporting information (6 pages, 6 figures

A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Detection of SARS-CoV-2 RNA in the Danube river in Serbia associated with the discharge of untreated wastewaters

In Serbia less than 13 % of collected municipal wastewaters is being treated before their release in the environment. This includes all municipal wastewater discharges from Belgrade (capital city of Serbia; population 1,700,000). Previous research has identified the impacts of raw wastewater discharges from Belgrade on the Danube River, and this study investigated if such discharges also provided a pathway for SARS-CoV-2 RNA material. Samples were collected during the most critical circumstances that occurred so far within the COVID-19 pandemics in Serbia. Grab and composite samples were collected in December 2020, during the peak of the third wave (in terms of reported cases) at the site which receives the wastewater loads in Belgrade. Grab samples collected upstream and downstream of Belgrade were also analyzed. RNA was quantified using RT-qPCR with primer sets targeting nucleocapsid (N1 and N2) and envelope (E) protein genes. SARS-CoV-2 RNA (5.97×103 to 1.32×104 copies/L) was detected only in samples collected at the site strongly impacted by the wastewaters where all three applied primer sets gave positive signals. Determined concentrations correspond to those reported in wastewater influents sampled at treatment plants in other countries indicating an epidemiological indicator function of used approach for rivers with high pollution loads in countries with poor wastewater treatment

The number of transmission channels through a single-molecule junction

We calculate transmission eigenvalue distributions for Pt-benzene-Pt and Pt-butadiene-Pt junctions using realistic state-of-the-art many-body techniques. An effective field theory of interacting $\pi$-electrons is used to include screening and van der Waals interactions with the metal electrodes. We find that the number of dominant transmission channels in a molecular junction is equal to the degeneracy of the molecular orbital closest to the metal Fermi level.Comment: 9 pages, 8 figure