5,875 research outputs found
Metallization of solid molecular hydrogen in two dimensions: Mott-Hubbard-type transition
We analyze the pressure-induced metal-insulator transition in a
two-dimensional vertical stack of molecules in x-y plane, and show that
it represents a striking example of the Mott-Hubbard-type transition. Our
combined exact diagonalization approach, formulated and solved in the second
quantization formalism, includes also simultaneous ab initio readjustment of
the single-particle wave functions, contained in the model microscopic
parameters. The system is studied as a function of applied side force
(generalized pressure), both in the -molecular and -quasiatomic states.
Extended Hubbard model is taken at the start, together with longer-range
electron-electron interactions incorporated into the scheme. The stacked
molecular plane transforms discontinuously into a (quasi)atomic state under the
applied force via a two-step transition: the first between molecular insulating
phases and the second from the molecular to the quasiatomic metallic phase. No
quasiatomic insulating phase occurs. All the transitions are accompanied by an
abrupt changes of the bond length and the intermolecular distance (lattice
parameter), as well as by discontinuous changes of the principal electronic
properties, which are characteristic of the Mott-Hubbard transition here
associated with the jumps of the predetermined equilibrium lattice parameter
and the effective bond length. The phase transition can be interpreted in terms
of the solid hydrogen metallization under pressure exerted by e.g., the
substrate covered with a monomolecular film of the vertically stacked
molecules. Both the Mott and Hubbard criteria at the insulator to metal
transition are discussed
Discontinuous transition of molecular-hydrogen chain to the quasi-atomic state: Exact diagonalization - ab initio approach
We obtain in a direct and rigorous manner a transition from a stable
molecular hydrogen single chain to the quasiatomic two-chain
state. We devise an original method composed of an exact diagonalization in the
Fock space combined with an ab initio adjustment of the single-particle wave
function in the correlated state. In this approach the well-known problem of
double-counting the interparticle interaction does not arise at all. The
transition is strongly discontinuous, and appears even for relatively short
chains possible to tackle, . The signature of the transition as a
function of applied force is a discontinuous change of the equilibrium
intramolecular distance. The corresponding change of the Hubbard ratio
reflects the Mott--Hubbard-transition aspect of the atomization. Universal
feature of the transition relation to the Mott criterion for the
insulator--metal transition is also noted. The role of the electron
correlations is thus shown to be of fundamental significance.Comment: 6 pages, 5 figures, 1 tabl
Combined shared and distributed memory ab-initio computations of molecular-hydrogen systems in the correlated state: process pool solution and two-level parallelism
An efficient computational scheme devised for investigations of ground state
properties of the electronically correlated systems is presented. As an
example, chain is considered with the long-range
electron-electron interactions taken into account. The implemented procedure
covers: (i) single-particle Wannier wave-function basis construction in the
correlated state, (ii) microscopic parameters calculation, and (iii) ground
state energy optimization. The optimization loop is based on highly effective
process-pool solution - specific root-workers approach. The hierarchical,
two-level parallelism was applied: both shared (by use of Open
Multi-Processing) and distributed (by use of Message Passing Interface) memory
models were utilized. We discuss in detail the feature that such approach
results in a substantial increase of the calculation speed reaching factor of
for the fully parallelized solution.Comment: 14 pages, 10 figures, 1 tabl
Metallization of atomic solid hydrogen within the extended Hubbard model with renormalized Wannier wave functions
We refer to our recent calculations (Eur. Phys. J. B, \textbf{86}, 252
(2013)) of metallization pressure of the three-dimensional simple-cubic crystal
of atomic hydrogen and study the effect on the crucial results concocting from
approximating the Slater-type orbital function with a series of
Gaussians. As a result, we find the critical metallization pressure $p_C = 102\
GPa$. The latter part is a discussion of the influence of zero-point motion on
the stabilizing pressure. We show that in our model the estimate magnitude of
zero-point motion carries a little effect on the critical metallization
pressure at zero temperature.Comment: 4 pages, 5 figures, 1 tabl
Entrepreneurship and Economic Growth: An Investigation into the Relationship between Entrepreneurship and Total Factor Productivity Growth in the EU
Endogenous growth theory assigns an important role for entrepreneurship in the process of economic development. This paper sets to formally test the impact of entrepreneurship on economic growth. Entrepreneurship is represented by a number of proxy variables, whereas Total Factor Productivity is used as a measure of economic growth. Panel data of 26 European countries repeatedly sampled over a period of 11 years is used to estimate a Random Effects model. This study finds that entrepreneurship contributes to growth moderately. It is not, nonetheless, a dominant force shaping changes in TFP growth rates. Business Birth Rate, Self-employment Rate, Business Investment and Labour Productivity Growth were all found to be highly significant. The article concludes that more encompassing measure of entrepreneurship needs to be developed, one that would reflect the complexity of the notion.entrepreneurship, total factor productivity, economic growth, the EU
On Keller's conjecture in dimension seven
A cube tiling of is a family of pairwise disjoint cubes
such that . Two cubes , are called a
twin pair if for some and
for every . In , Keller conjectured that in
every cube tiling of there is a twin pair. Keller's conjecture
is true for dimensions and false for all dimensions . For
the conjecture is still open. Let , , and
let be the set of all th coordinates of vectors
such that and . It is
known that if for some and every or for some and , then
Keller's conjecture is true for . In the present paper we show that it is
also true for if for some and . Thus, if there is a counterexample to Keller's conjecture in dimension
seven, then for some and .Comment: 37 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1304.163
- …