Soft Carrier Multiplications by Hot Electrons in Graphene

By using Boltzmann formalism, we show that carrier multiplication by impact ionization can take place at relatively low electric fields during electronic transport in graphene. Because of the absence of energy gap, this effect is not characterized by a field threshold unlike in conventional semiconductors, but is a quadratic function of the electric field. We also show that the resulting current is an increasing function of the electronic temperature, but decreases with increasing carrier concentration

Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids

A quantum Monte Carlo method that combines the second-order many-body perturbation theory and Monte Carlo (MC) integration has been developed for correlation and correlation-corrected (quasiparticle) energy bands of one-dimensional solids. The sum-of-product expressions of correlation energy and self-energy are transformed, with the aid of a Laplace transform, into high-dimensional integrals, which are subject to a highly scalable MC integration with the Metropolis algorithm for importance sampling. The method can compute correlation energies of polyacetylene and polyethylene within a few mEh and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.open0

Stochastic evaluation of second-order Dyson self-energies

A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Greens function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 108 Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.open9

Thermodynamic Tree: The Space of Admissible Paths

Is a spontaneous transition from a state x to a state y allowed by thermodynamics? Such a question arises often in chemical thermodynamics and kinetics. We ask the more formal question: is there a continuous path between these states, along which the conservation laws hold, the concentrations remain non-negative and the relevant thermodynamic potential G (Gibbs energy, for example) monotonically decreases? The obvious necessary condition, G(x)\geq G(y), is not sufficient, and we construct the necessary and sufficient conditions. For example, it is impossible to overstep the equilibrium in 1-dimensional (1D) systems (with n components and n-1 conservation laws). The system cannot come from a state x to a state y if they are on the opposite sides of the equilibrium even if G(x) > G(y). We find the general multidimensional analogue of this 1D rule and constructively solve the problem of the thermodynamically admissible transitions. We study dynamical systems, which are given in a positively invariant convex polyhedron D and have a convex Lyapunov function G. An admissible path is a continuous curve along which $G$ does not increase. For x,y from D, x\geq y (x precedes y) if there exists an admissible path from x to y and x \sim y if x\geq y and y\geq x. The tree of G in D is a quotient space D/~. We provide an algorithm for the construction of this tree. In this algorithm, the restriction of G onto the 1-skeleton of $D$ (the union of edges) is used. The problem of existence of admissible paths between states is solved constructively. The regions attainable by the admissible paths are described.Comment: Extended version, 31 page, 9 figures, 69 cited references, many minor correction

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials