Using density functional theory calculations, we have studied the edge-functionalization of armchair graphene nanoribbons (AGNRs) with pentagonal-hexagonal edge structures. While the AGNRs with pentagonal-hexagonal edge structures (labeled (5,6)-AGNR
s) are metallic, the edge-functionalized (5,6)-AGNRs with substitutional atoms opens a band gap. We find that the band structures of edge-functionalized (5,6)-N-AGNRs by substitution resemble those of defect-free (N-1)-AGNR at the {Gamma} point, whereas those at the X point show the original ones of the defect-free N-AGNR. The overall electronic structures of edge-functionalized (5,6)-AGNRs depend on the number of electrons, supplied by substitutional atoms, at the edges of functionalized (5,6)-AGNRs.
The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical da
ta to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between in-sample volatility and out-of-sample volatility decreases, but also the out-of-sample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance.
We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, $(hat a^{dagger})^2$, where $hat a^dagger$ is the photon creation operator. We compare it with a previous pr
oposal using the photon addition-then-subtraction, $hat a hat a^dagger$, where $hat a$ is the photon annihilation operator, that works as an appropriate amplifier only for weak light fields. We show that when the amplitude of a coherent state is $|alpha| gtrsim 0.91$, the $(hat a^{dagger})^2$ operation serves as a more efficient amplifier compared to the $hat a hat a^dagger$ operation in terms of equivalent input noise. Using $hat a hat a^dagger$ and $(hat a^{dagger})^2$ as basic building blocks, we compare combinatorial amplifications of coherent states using $(hat a hat a^dagger)^2$, $hat a^{dagger 4}$, $hat a hat a^daggerhat a^{dagger 2}$, and $hat a^{dagger 2}hat a hat a^dagger$, and show that $(hat a hat a^dagger)^2$, $hat a^{dagger 2}hat a hat a^dagger$, and $hat a^{dagger 4}$ exhibit strongest noiseless properties for $|alpha| lesssim 0.51$, $0.51 lesssim |alpha| lesssim 1.05 $, and $|alpha|gtrsim 1.05 $, respectively. We further show that the $(hat a^{dagger})^2$ operation can be used for amplifying superpositions of the coherent states. In contrast to previous studies, our work provides efficient schemes to implement a noiseless amplifier for light fields with medium and large amplitudes.
Proper inclusion of van der Waals (vdW) interactions in theoretical simulations based on standard density functional theory (DFT) is crucial to describe the physics and chemistry of systems such as organic and layered materials. Many encouraging appr
oaches have been proposed to combine vdW interactions with standard approximate DFT calculations. Despite many vdW studies, there is no consensus on the reliability of vdW methods. To help further development of vdW methods, we have assessed various vdW functionals through the calculation of structural prop- erties at equilibrium, such as lattice constants, bulk moduli, and cohesive energies, for bulk solids, including alkali, alkali-earth, and transition metals, with BCC, FCC, and diamond structures as the ground state structure. These results provide important information for the vdW-related materials research, which is essential for designing and optimizing materials systems for desired physical and chemical properties.
We compare three different types of optical qubits for information transfer via quantum teleportation and direction transmission under photon losses. The three types of qubits are (1) qubits using the vacuum and the single-photon (VSP) states, (2) si
ngle-photon qubits using polarization degrees of freedom, i.e., polarized single-photon (PSP) qubits, and (3) coherent-state qubits that use two coherent states with opposite phases as the qubit basis. Our analysis shows that the teleportation scheme outperforms the direct transmission for most of cases as far as fidelities are concerned. Overall, VSP qubits are found to be the most efficient for both the direct transmission and teleportation under photon loss effects. The coherent-state qubits are more robust than PSP qubits either when their amplitudes are small as $|alpha| lesssim 1.22$ or when photon loss effects are strong. Our results would provide useful and timely information for the development of practical optical quantum information processing particularly in the context of hybrid architectures.
Using density functional theory, we study physical properties of boron nitride nanotubes (BNNTs) with the substitutional carbon pair defect. We also consider the Stone-Wales (SW) rearrangement of the C-C pair defect in the BNNT. The formation energy
of an SW defect of the carbon dimer is approximately 3.1 eV lower than that of the SW-transformed B-N pair in the undoped BNNT. The activation energies show that the SW defect in the C-doped BNNT may be experimentally observed with a higher probability than in the undoped BNNT. Finally, we discuss the localized states originating from the carbon pair impurities.
