A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and its Applications

We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume. Focusing on the distribution of positions of the particles, we have point processes of the fixed number of points in a bounded domain. By taking the thermodynamic limit such that the particle density converges to a finite value, the boson/fermion processes are obtained. This argument is a realization of the equivalence of ensembles, since resulting processes are considered to describe a grand canonical ensemble of points. Random point processes corresponding to para-particles of order two are discussed as an application of the formulation. A statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.Comment: 26pages, Some typos are corrected, to be published in Commun. Math. Phy

Relation between dispersion lines and conductance of telescoped armchair double-wall nanotubes analyzed using perturbation formulas and first-principles calculations

The Landauer's formula conductance of the telescoped armchair nanotubes is calculated with the Hamiltonian defined by first-principles calculations (SIESTA code). Herein, partially extracting the inner tube from the outer tube is called 'telescoping'. It shows a rapid oscillation superposed on a slow oscillation as a function of discrete overlap length $(L-1/2)a$ with an integer variable $L$ and the lattice constant $a$. Considering the interlayer Hamiltonian as a perturbation, we obtain the approximate formula of the amplitude of the slow oscillation as $|A|^2/(|A|^2+\varepsilon^2)$ where $A$ is the effective interlayer interaction and $\varepsilon$ is the band split without interlayer interaction. The approximate formula is related to the Thouless number of the dispersion lines.Comment: 9 figure

Analysis of quantum conductance of carbon nanotube junctions by the effective mass approximation

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.Comment: RevTe

Backward diode composed of a metallic and semiconducting nanotube

The conditions necessary for a nanotube junction connecting a metallic and semiconducting nanotube to rectify the current are theoretically investigated. A tight binding model is used for the analysis, which includes the Hartree-Fock approximation and the Green's function method. It is found that the junction has a behavior similar to the backward diode if the gate electrode is located nearby and the Fermi level of the semiconducting tube is near the gap. Such a junction would be advantageous since the required length for the rectification could be reduced.Comment: 4 pages, RevTeX, uses epsf.st

Band structures of periodic carbon nanotube junctions and their symmetries analyzed by the effective mass approximation

The band structures of the periodic nanotube junctions are investigated by the effective mass theory and the tight binding model. The periodic junctions are constructed by introducing pairs of a pentagonal defect and a heptagonal defect periodically in the carbon nanotube. We treat the periodic junctions whose unit cell is composed by two kinds of metallic nanotubes with almost same radii, the ratio of which is between 0.7 and 1 . The discussed energy region is near the undoped Fermi level where the channel number is kept to two, so there are two bands. The energy bands are expressed with closed analytical forms by the effective mass theory with some assumptions, and they coincide well with the numerical results by the tight binding model. Differences between the two methods are also discussed. Origin of correspondence between the band structures and the phason pattern discussed in Phys. Rev. B {\bf 53}, 2114, is clarified. The width of the gap and the band are in inverse proportion to the length of the unit cell, which is the sum of the lengths measured along the tube axis in each tube part and along 'radial' direction in the junction part. The degeneracy and repulsion between the two bands are determined only from symmetries.Comment: RevTeX, gif fil

Topological Phases in Graphitic Cones

The electronic structure of graphitic cones exhibits distinctive topological features associated with the apical disclinations. Aharonov-Bohm magnetoconductance oscillations (period Phi_0) are completely absent in rings fabricated from cones with a single pentagonal disclination. Close to the apex, the local density of states changes qualitatively, either developing a cusp which drops to zero at the Fermi energy, or forming a region of nonzero density across the Fermi energy, a local metalization of graphene.Comment: 4 pages, RevTeX 4, 3 PostScript figure

Phonon-driven ultrafast exciton dissociation at donor-acceptor polymer heterojunctions

A quantum-dynamical analysis of phonon-driven exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parameterized for three electronic states and 24 vibrational modes. Two interfering decay pathways are identified: a direct charge separation, and an indirect pathway via an intermediate bridge state. Both pathways depend critically on the dynamical interplay of high-frequency C=C stretch modes and low-frequency ring-torsional modes. The ultrafast, highly non-equilibrium dynamics is consistent with time-resolved spectroscopic observations

Cosmic Chemical Evolution

Numerical simulations of standard cosmological scenarios have now reached the degree of sophistication required to provide tentative answers to the fundamental question: Where and when were the heavy elements formed? Averaging globally, these simulations give a metallicity that increases from 1% of the solar value at $z=3$ to 20% at present. This conclusion is, in fact, misleading, as it masks the very strong dependency of metallicity on local density. At every epoch higher density regions have much higher metallicity than lower density regions. Moreover, the highest density regions quickly approach near solar metallicity and then saturate, while more typical regions slowly catch up. These results are much more consistent with observational data than the simpler picture (adopted by many) of gradual, quasi-uniform increase of metallicity with time.Comment: ApJ(Letters) in press, 15 latex pages and 4 figure