Related papers: Optimally localized Wannier functions for quasi on…
Position scaling-eigenfunctions are generated by transforming compactly supported orthonormal scaling functions and utilized for faster alternatives to maximally localized Wannier functions (MLWFs). The position scaling-eigenfunctions are…
Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a…
We systematically construct flatbands (FB) for tight-binding models on simple Bravais lattices in space dimension $d \geq 2$ in the presence of a static uniform DC field. Commensurate DC field directions yield irreducible Wannier-Stark (WS)…
The dependence of the localization length on the number of occupied subbands $N$ in low-dimensional semiconductors is investigated. The localization length is shown to be proportional to the number of occupied subbands in…
We exhibit limit-periodic Schr\"odinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of…
An exact WKB treatment of 1-d homogeneous Schr\"odinger operators (with the confining potentials $q^N$, $N$ even) is extended to odd degrees $N$. The resulting formalism is first illustrated theoretically and numerically upon the spectrum…
According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of…
We study the spectral properties of ergodic Schr\"{o}dinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go…
The effect of Kolmogorov-Arnold-Moser (KAM) theorem in quantum systems is manifested in dividing eigenstates into regular and irregular states. We propose an effective method based on Wannier basis in phase space to illustrate this division…
We study multi-frequency quasi-periodic Schr\"odinger operators on $\mathbb{Z}$ in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's semi-algebraic elimination of multiple resonances with the…
We present an ab initio inelastic quantum transport approach based on maximally localized Wannier functions. Electronic-structure properties are calculated with density-functional theory in a planewave basis, and electron-vibration coupling…
Optimal tuning of functional parameters in density functional theory approximations, based on enforcing the ionization potential theorem, has emerged as the method of choice for the non-empirical prediction of the electronic structure of…
An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process…
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave…
The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum…
The BR, formulated by Zak in the 80s, is widely used in studies of topological phase of material. EBR are considered the building block of TQC. However, there were debate on whether they admit split bands, or if they contain band invariant…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
The convergence of the Rayleigh-Ritz method with nonlinear parameters optimized through minimization of the trace of the truncated matrix is demonstrated by a comparison with analytically known eigenstates of various quasi-solvable systems.…
We prove that localization near band edges of multi-dimensional ergodic random Schr\"odinger operators with periodic background potential in $L^2(\mathbb{R}^d)$ is universal. By this we mean that localization in its strongest dynamical form…
We present the exact diagonalization of the Schrodinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations…