A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.Comment: 7 pages, latex, no figures, To appear in J. Phys

Multi-terminal Electron Transport Through Single Phenalenyl Molecule: A Theoretical Study

We do parametric calculations to elucidate multi-terminal electron transport properties through a molecular system where a single phenalenyl molecule is attached to semi-infinite one-dimensional metallic leads. A formalism based on the Green's function technique is used for the calculations while the model is described by tight-binding Hamiltonian. We explore the transport properties in terms of conductance, reflection probability as well as current-voltage characteristic. The most significant feature we articulate is that all these characteristics are very sensitive to the locations where the leads are connected and also the molecule-to-lead coupling strengths. The presence of other leads also has a remarkable effect on these transport properties. We study these phenomena for two-, three- and four-terminal molecular systems. Our numerical study may be utilized in designing tailor-made molecular electronic devices.Comment: 13 pages, 15 figure

Motion of the hydrogen bond proton in cytosine and the transition between its normal and imino states

The potential energy surface of the H13 proton in base cytosine of the DNA molecules is calculated {\it ab initio} at the Gaussian98 MP2/6-311G(d,p) level. Two potential wells are found. One corresponds to the normal cytosine, while the other corresponds to its imino tautomer. The bindings of the proton in these wells are stable enough against the thermo-disturbance. The motions of the proton in these wells are oscillations around the nearest nitrogen atom like the pendula, and may move far away from the nitrogen atom to form the hydrogen bond with other bases. The estimated tunneling probability of the H13 proton from one well to another well shows that the life time of the proton staying in one of these wells is about 6$\times10^2$ yr. It is too long to let tautomers of cytosine be in thermodynamical equilibrium in a room temperature gas phase experiment. The biological significance of these result is discussed.Comment: 4 pages, 4 figures, replace the bmp files in figures 1 and 2 by corresponding eps files in tex

Adiabatic Quantum Computing for Random Satisfiability Problems

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables, the adiabatic method gives solution probabilities close to 1 for problem sizes feasible to evaluate via simulation on current computers. However, for these sizes the minimum energy gaps of most instances are fairly large, so the good performance scaling seen for small problems may not reflect asymptotic behavior where costs are dominated by tiny gaps. Moreover, the resulting search costs are much higher than for other methods. Variants of the quantum algorithm that do not match the adiabatic limit give lower costs, on average, and slower growth than the conventional GSAT heuristic method.Comment: added discussion of discrete adiabatic method, and simulations with 30 bits 8 pages, 8 figure

Inter-cluster reactivity of Metallo-aromatic and anti-aromatic Compounds and Their Applications in Molecular Electronics: A Theoretical Investigation

Local reactivity descriptors such as the condensed local softness and Fukui function have been employed to investigate the inter-cluster reactivity of the metallo-aromatic (Al4Li- and Al4Na-) and anti-aromatic (Al4Li4 and Al4Na4) compounds. We use the concept of group softness and group Fukui function to study the strength of the nucleophilicity of the Al4 unit in these compounds. Our analysis shows that the trend of nucleophilicity of the Al4 unit in the above clusters is as follows; Al4Li- > Al4Na- > Al4Li4 > Al4Na 4 For the first time we have used the reactivity descriptors to show that these clusters can act as electron donating systems and thus can be used as a molecular cathode.Comment: 23 pages, 1 figure and 1 table of conten

Studies in perturbation theory. XI - Lower bounds to energy eigenvalues, ground state and excited states

Upper and lower bounds determined for energy eigenvalues using Hamiltonian operators and projections on manifolds in Hilbert region

Studies in perturbation theory. x- lower bounds to energy eigenvalues in perturbation theory

Low bounds to energy eigenvalues in quantum theory problems by partitioning technique for positive perturbatio

Quantum theory of time-dependent phenomena treated by the evolution operator technique

Time dependent phenomena in nonrelativistic quantum theory treated by evolution operator techniqu

Bose-Einstein condensation of correlated atoms in a trap

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of Jastrow type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean square radius and kinetic energy are also given.Comment: 14 pages, 19 figures, 1 Table, RevTe

Linear algebra and the fundaments of quantum theory

Fundamental quantum theory formulations using axioms of linear algebr