相关论文: Band theory in the context of the Hamilton-Jacobi …

Orbital susceptibility for Bloch electrons is calculated for the first time up to the first order with respect to overlap integrals between the neighboring atomic orbitals, assuming single-band models. A general and rigorous theory of…

We investigate the localization properties of independent electrons in a periodic background, possibly including a periodic magnetic field, as e.g. in Chern insulators and in Quantum Hall systems. Since, generically, the spectrum of the…

We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…

A new method for the localization of crystalline orbitals for entangled energy bands is proposed. It is an extension of the Wannier-Boys algorithm [C. M. Zicovich-Wilson, R. Dovesi, and V. R. Saunders, J. Chem. Phys. 115, 9708 (2001)] which…

An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in…

We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine…

A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy periodic with the lattice contains the first reciprocal lattice vector G1 =…

We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians. In this paper we focus on problems that have a two parameter search space in the bootstrap approach: the double well and a periodic potential…

The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau…

By using a recently derived upper bound on the allowed equilibrium current in a ring, it is proved that the magnitude of the group velocity of a Bloch electron in a one-dimensional periodic potential is always less than or equal to the…

Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an…

We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in…

In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane.…

There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…

We study the nonlinear Schr\"odinger equation with a periodic delta-function potential. This realizes a nonlinear Kr\"onig-Penney model, with physical applications in the context of trapped Bose-Einstein condensate alkaly gases and in the…

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…

By means of a generalization of the Fefferman-de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a specific class of lowest Landau band wave…

Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The…

We extend previous work applying elementary matrix mechanics to one-dimensional periodic arrays (to generate energy bands) to two-dimensional arrays. We generate band structures for the square lattice "2D Kronig-Penney model" (square…