Related papers: Effective mass theorems with Bloch modes crossings
Solutions to the Schr\"{o}dinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the…
A method for homogenization of a heterogeneous (finite or periodic) elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations.…
The Floquet-Bloch theorem allows waves in infinite, lossless periodic media to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is challenged under the realistic constraints of loss and finite extent. In this work, we…
A theoretical model is used to study water waves propagating into and through a region containing thin floating ice, for ice covers transitioning from consolidated (large floe sizes) to fully broken (small floe sizes). The degree of…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
We present a detailed analysis of the dynamics of Bloch oscillations of Bose-Einstein condensates in disordered lattice potentials. Due to the disorder and the interparticle interactions these oscillations undergo a dephasing, reflected in…
We consider two-dimensional Schroedinger equations with honeycomb potentials and slow time-periodic forcing of the form: $$i\psi_t (t,x) = H^\varepsilon(t)\psi=\left(H^0+2i\varepsilon A (\varepsilon t) \cdot \nabla \right)\psi,\quad…
In the Bloch-wave approach to estimate the baryon-number-violating scattering cross section in the standard electroweak theory in the laboratory, we clarify the relation between the single sphaleron barrier and multiple (near periodic)…
A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schr\"odinger equation shows that the…
Floquet theory has spawned many exciting possibilities for electronic structure control with light with enormous potential for future applications. The experimental realization in solids, however, largely remains pending. In particular, the…
We investigate an oblique spacetime crystal realized by a monoatomic crystal in which a mode of sound propagates. We provide a systematic analysis of the crystal and obtain the corresponding band structure, based on which the electron…
We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…
We ask the question 'what happens to Bloch waves in gratings synthetically moving at near the speed of light?'. First we define a constant refractive index (CRI) model in which Bloch waves remain well defined as they break the light…
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time…
We have studied the bound states of the extra electron in a molecular wire, corresponding to the physical situation of the electron tunneling through the wire. Based on formalism of the scattering operator that accounts for many-electron…
We investigate the dynamics of Bloch electrons using a density operator method and connect this approach with previous theories based on wave packets. We study non-interacting systems with negligible disorder and strong spin-orbit…
We study the semiclassical dynamics of interacting electrons in a biased crystal lattice. A complex dynamical scenario emerges from the interplay between the Coulomb and the external electric fields. When the electrons are far apart, the…
The small dispersion limit of the focusing nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. First, through a comprehensive set of numerical simulations, it is demonstrated that…
We theoretically study the elastic deformation of a fluid membrane induced by an adhering spherical colloidal particle within the framework of a Helfrich energy. Based on a full optimization of the membrane shape we find a continuous…