相关论文: Noninteracting Electrons in a Prototypical One-Dim…
In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential,…
All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the…
One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite…
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or…
We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch…
The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…
We consider a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field. This problem is periodic both in space and time and can be solved analytically…
The coupled nonequilibrium dynamics of electrons and phonons in monolayer MoS2 is investigated by combining first-principles calculations of the electron-phonon and phonon-phonon interaction with the time-dependent Boltzmann equation.…
We study the effect of a one dimensional periodic potential on the dynamic structure factor of an interacting Bose Einstein condensate at zero temperature. We show that, due to phononic correlations, the excitation strength towards the…
We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a…
The band structures describing non-interacting particles in one-dimensional superlattices of arbitrary periodicity are obtained by an analytical diagonalization of the Hamiltonian without adopting the popular tight-binding approximation.…
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…
In the present Letter we use the Wannier function basis to construct lattice approximations of the nonlinear Schr\"{o}dinger equation with a periodic potential. We show that the nonlinear Schr\"{o}dinger equation with a periodic potential…
We report on the experimental investigation of the response of a three-dimensional Bose-Einstein condensate (BEC) in the presence of a one-dimensional (1D) optical lattice. By means of Bragg spectroscopy we probe the band structure of the…
We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of…
While kinetic energy of a massive particle generally has quadratic dependence on its momentum, a flat, dispersionless energy band is realized in crystals with specific lattice structures. Such macroscopic degeneracy causes the emergence of…
Theoretical quest of flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be…
We investigate the electronic properties of two-dimensional electron gases (2DEGs) subjected to a periodic patterned gate. By incorporating the superlattice (SL) potential induced by patterning into the Schrodinger equation, we develop a…
In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…