Related papers: Extended electronic states in disordered 1-d latti…
We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized…
We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…
We study systematically the period-doubled Bloch states for a weakly interacting Bose-Einstein condensate in a one-dimensional optical lattice. This kind of state is of form $\psi_k=e^{ikx}\phi_k(x)$, where $\phi_k(x)$ is of period twice…
We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states…
Non-Hermitean operators may appear during the calculation of a partition function in various models of statistical mechanics. The tail eigen-states, having anomalously small real part of energy $Re(\eps)$, became naturally important in this…
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
We consider disordered tight-binding models which Green's functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D_{1} that…
We examined the characteristics of a metal-insulator transition on a two-dimensional non-bipartite lattice when both disorders and electron interactions are present. Using a real-space renormalization group method and finite-size scaling…
In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasi-periodical potentials and coupling constants. On the other hand, mobility…
Eigenvector continuation (EC) has recently attracted a lot attention in nuclear structure and reactions as a variational resummation tool for many-body expansions. While previous applications focused on ground-state energies, excited states…
We propose an explanation of the bands of extended states appearing in random one dimensional models with correlated disorder, focusing on the Continuous Random Dimer model [A.\ S\'{a}nchez, E.\ Maci\'a, and F.\ Dom\'\i nguez-Adame, Phys.\…
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…
A general scheme is developed to deal with 1D lattice systems that could be topologically complicated. It is aimed to give a complete study of two coupled normal metal rings. Our method starts with an investigation of the local expressions…
We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) \sim…
The one-electron properties of a certain class of one-dimensional ternary quasicrystals are investigated. In particular, we show in detail the presence of a special kind of critical states called marginal critical states in these QCs. By…
We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control…
Based on the so called $t$-$\phi$ model in two-dimensional (2D) lattices, we investigate the stabilities of a class of extended staggered-flux (SF) phases (which are the extensions of the $\sqrt{2}\times\sqrt{2}$ SF phase to generalized…
We present a novel model to calculate single-electron states in random quantum dot superlattices made of wide-gap semiconductors. The source of disorder comes from the random arrangement of the quantum dots (configurational disorder) as…
We present an analytical method for finding all the electronic eigenfunctions and eigenvalues of the aperiodic Thue-Morse lattice. We prove that this system supports only extended electronic states which is a very unusual behavior for this…
We constructed an electrical circuit to realize a modified Haldane lattice exhibiting the unusual phenomenon of antichiral edge states. The circuit consists of a network of inductors and capacitors with interconnections reproducing the…