An introduction to the elements of algebra, designed for the use of those who are acquainted only with the first principles of arithmetic.

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"Unto this last": four essays on the first principles of political economy.

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The first principles of evolution,

"Literature": p. 321-328.

First principles.

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First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

First-principles calculation of P-type alloy scattering in Si1-xGex

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

Functionalized adamantane: Building blocks for nanostructure self-assembly

We report first-principles calculations on the electronic and structural properties of chemically functionalized adamantane molecules, either in isolated or crystalline forms. Boron and nitrogen functionalized molecules, aza-, tetra-aza-, bora-, and tetra-bora-adamantane, were found to be very stable in terms of energetics, consistent with available experimental data. Additionally, a hypothetical molecular crystal in a zincblende structure, involving the pair tetra-bora-adamantane and tetra-aza-adamantane, was investigated. This molecular crystal presented a direct and large electronic band gap and a bulk modulus of 20 GPa. The viability of using those functionalized molecules as fundamental building blocks for nanostructure self-assembly is discussed.

Signatures of oxygen on Cu(3)Au(100): From isolated impurity to oxide regimes

We analyze the scanning tunneling microscopy (STM) signatures for the O/Cu(3)Au(100) surface from the low-coverage (isolated impurity) to high-coverage (oxide) regimes. First-principles calculations show that oxygen signatures switch from dark to bright spots as the oxygen coverage increases. This behavior is nicely traced back to a change in the oxygen orbital character of the Fermi-level electronic states. Our results allow for the chemical identification by STM of oxygen and copper atoms in the fully ordered O/Cu(3)Au(100)-c(2x2) surface.

Bilayer graphene dual-gate nanodevice: An ab initio simulation

We study the electronic transport properties of a dual-gated bilayer graphene nanodevice via first-principles calculations. We investigate the electric current as a function of gate length and temperature. Under the action of an external electrical field we show that even for gate lengths up 100 angstrom, a nonzero current is exhibited. The results can be explained by the presence of a tunneling regime due the remanescent states in the gap. We also discuss the conditions to reach the charge neutrality point in a system free of defects and extrinsic carrier doping.

Mimicking nanoribbon behavior using a graphene layer on SiC

We propose a natural way to create quantum-confined regions in graphene in a system that allows large-scale device integration. We show, using first-principles calculations, that a single graphene layer on a trenched region of [000 (1) over bar] SiC mimics (i) the energy bands around the Fermi level and (ii) the magnetic properties of free-standing graphene nanoribbons. Depending on the trench direction, either zigzag or armchair nanoribbons are mimicked. This behavior occurs because a single graphene layer over a SiC surface loses the graphenelike properties, which are restored solely over the trenches, providing in this way a confined strip region.

Ferromagnetic coupling in a Co-doped graphenelike ZnO sheet

Using first-principles calculations it is demonstrated that Co doped graphenelike ZnO sheet presents ferromagnetic coupling. The Co atoms are energetically barrierless absorbed in the Zn sites, suffering a Jahn-Teller distortion. The results reveal that the origin of the ferromagnetic coupling, different from the bulk 3D ZnO stacking, is mainly guided by a direct exchange interaction without any additional defect. This ferromagnetic coupling is due to the system topology, namely, it is a direct consequence of the two-dimensional character of the ZnO monolayer within graphenelike structure. Increasing the number of ZnO layers the ferromagnetic coupling vanishes.

Ab initio study of NOx compounds adsorption on SnO2 surface

An ab initio study of the adsorption processes on NOx compounds on (1 1 0) SnO2 surface is presented with the aim of providing theoretical hints for the development of improved NOx gas sensors. From first principles calculations (DFT¿GGA approximation), the most relevant NO and NO2 adsorption processes are analyzed by means of the estimation of their adsorption energies. The resulting values and the developed model are also corroborated with experimental desorption temperatures for NO and NO2, allowing us to explain the temperature-programmed desorption experiments. The interference of the SO2 poisoning agent on the studied processes is discussed and the adsorption site blocking consequences on sensing response are analyzed.

Defect study of SnO2 nanostructures by cathodoluminescence analysis: Application to nanowires

Defects in SnO2 nanowires have been studied by cathodoluminescence, and the obtained spectra have been compared with those measured on SnO2 nanocrystals of different sizes in order to reveal information about point defects not determined by other characterization techniques. Dependence of the luminescence bands on the thermal treatment temperatures and pre-treatment conditions have been determined pointing out their possible relation, due to the used treatment conditions, with the oxygen vacancy concentration. To explain these cathodoluminescence spectra and their behavior, a model based on first-principles calculations of the surface oxygen vacancies in the different crystallographic directions is proposed for corroborating the existence of surface state bands localized at energy values compatible with the found cathodoluminescence bands and with the gas sensing mechanisms. CL bands centered at 1.90 and 2.20 eV are attributed to the surface oxygen vacancies 100° coordinated with tin atoms, whereas CL bands centered at 2.37 and 2.75 eV are related to the surface oxygen vacancies 130° coordinated. This combined process of cathodoluminescence and ab initio calculations is shown to be a powerful tool for nanowire defect analysis.