Article history: Received 26 October 2015 Received in revised form 8 June 2016 Accepted 21 July 2016 Available online 27 July 2016

We consider the real-time evolution of Hubbard model in limit infinite coupling. In this Hamiltonian system is mapped into a number-conserving quadratic form spinless fermions, i.e. tight binding model. The relevant local observables, however, do not transform well under mapping and take very complicated expressions terms fermions. Here we show that for two classes interesting observables quenc...

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a lattice Zd with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

Self-consistent tight binding molecular dynamics studies of TiO2 anatase and rutile nanoclusters in dissociable water are reported. It is found that the structure of the particle expands as a result of interaction between the particle’s surface and water. Water molecules dissociate at the nanoparticle surface during simulation. ! 2007 Elsevier B.V. All rights reserved.

Walkup’s class K(d) consists of the d-dimensional simplicial complexes all whose vertex links are stacked (d − 1)-spheres. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic χ satisfies f1 ≥ 5f0 − 15 2 χ, with equality only for X ∈ K(4). Kühnel observed that this implies f0(f0− 11) ≥ −15χ, with equality only for 2-neighborly members of K(...

We consider a quantum two-particle system on a lattice Z with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann’s lemma.

In this paper we consider a new superlattice system consisting of alternating layers of CdTe and HgTe constructed parallel to the (001) zincblende plane. The tight-binding method is used to calc~late the electronic properties of this system, in particular, band edge and interface properties. The energy gap as a function of layer thickness is determined. It is found to decrease monotonically wit...

In relationships too, the associations are not static and but are constantly evolving in response to their environment. It could include all degrees of repulsion and antagonisms to affinity, from tight symbiosis of bacteria with their host eukaryotic cells to more loosely bound partnerships between entirely separate organisms. The article examines some examples of interactions at different leve...

We give a short summary of the fixed-energy Multi-Scale Analysis (MSA) of the Anderson tight binding model in dimension d ≥ 1 and show that this technique admits a straightforward extension to multi-particle systems. We hope that this short note may serve as an elementary introduction to the MSA.

A double-loop digraph G(N ; s1, s2) = G(V,E) is defined by V = ZN and E = {(i, i + s1), (i, i + s2)| i ∈ V }, for some fixed steps 1 ≤ s1 < s2 < N with gcd(N, s1, s2) = 1. Let D(N ; s1, s2) be the diameter of G and let us define D(N) = min 1≤s1<s2<N, gcd(N,s1,s2)=1 D(N ; s1, s2), D1(N) = min 1<s<N D(N ; 1, s). Some early works about the diameter of these digraphs studied the minimization of D(N...