Related papers: Effective mass theorems with Bloch modes crossings
In this paper we first derive a Coulomb Hamiltonian for electron--electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix.…
Low-energy electrons scattered in the conduction band of a dielectric solid should behave like Bloch electrons and will interact with perturbations of the atomic lattice, i.e. with phonons. Thus the phonon-based description of low-energy…
Large-momentum-transfer techniques are instrumental for the next generation of atom interferometers as they significantly improve their sensitivity. State-of-the-art implementations rely on elastic scattering processes from optical lattices…
The defect corrections to polarization and dielectric functions of Bloch electrons in quantum wells are first calculated. Following this, we derive the first two moment equations from Boltzmann transport theory and apply them to explore…
Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a…
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…
We investigate the interplay of disorder and interactions in the accelerated transport of a Bose-Einstein condensate through an incommensurate optical lattice. We show that interactions can effectively cancel the damping of Bloch…
A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum…
We quantify nonergodic and aging behaviors of nanocrystals (or quantum dots) based on stochastic model. Ergodicity breaking is characterized based on time average intensity and time average correlation function, which remain random even in…
Inspired by recent experiments with cold atoms in optical lattices, we consider a St\"uckelberg interferometer for a particle performing Bloch oscillations in a tight-binding model on the honeycomb lattice. The interferometer is made of two…
We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch functions. Starting from a…
We study the scattering of an electron from a one dimensional inverted Gaussian atomic potential in the presence of strong time periodic electric fields. Using Floquet theory, we construct the Floquet Scattering matrix in the…
The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent,…
The multiple scattering formalism is proposed describing the guided modes in the optical waveguide array within the framework of macroscopic electrodynamics. It is shown that, under sufficiently general assumptions, our approach justifies…
We investigate the large time behavior of the solutions to the nonlinear focusing Schr\"odinger equation with a time-dependent damping in the energy sub-critical regime. Under non classical assumptions on the unsteady damping term, we prove…
Periodically driven systems, characterised by their inherent non-equilibrium dynamics, are ubiquitously found in both classical and quantum regimes. In the field of photonics, these Floquet systems have begun to provide insight into how…
Bloch waves and Bloch band of Bose-Einstein Condensates in optical lattices are studied. We provide further evidence for the loop structure in the Bloch band, and compute the critical values of the mean-field interaction strength for the…
Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, $E \propto t^{\eta}$ with $\eta=0.46(2)$, and compressed-exponential momentum…
Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We…
Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that…