Related papers: Bloch oscillations in two-dimensional crystals: In…

Cold atoms in an optical lattice execute Bloch-Zener oscillations when they are accelerated. We have performed a theoretical investigation into the case when the optical lattice is the intra-cavity field of a driven Fabry-Perot resonator.…

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr\"ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum…

We study the Bloch oscillations (BOs) of two-component Bose-Einstein condensates (BECs) trapped in spin-dependent optical lattices. Based on the derived equations of motion of the wave packet in the basis of localized wave functions of the…

Bloch-Zener oscillations (BZO), i.e. the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external dc force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian…

In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…

Louis deBroglie's connection between momentum and spatial-frequency vectors is perhaps most viscerally-experienced via the real-time access that electron-diffraction provides to transverse slices of a nano-crystal's reciprocal-lattice. The…

Artificial Neural Networks (ANNs) are computational models inspired by the central nervous system (especially the brain) of animals and are used to estimate or generate unknown approximation functions relied on large amounts of inputs.…

The logcosh loss function for neural networks has been developed to combine the advantage of the absolute error loss function of not overweighting outliers with the advantage of the mean square error of continuous derivative near the mean,…

Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…

We discuss the quantum phase transition from the Mott-insulator state to the density-wave state for cold Bose atoms in a 2D square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small…

The model presented in this research predicts ideal chiral crystal and propose a new direction of designing chiral crystals. Skyrmions are topologically protected and structurally assymetric materials with an exotic spin composition. This…

Essentials of the scientific discovery process have remained largely unchanged for centuries: systematic human observation of natural phenomena is used to form hypotheses that, when validated through experimentation, are generalized into…

Time series datasets often have missing or corrupted entries, which need to be ignored in subsequent data analysis. For example, in the context of space physics, calibration issues, satellite telemetry issues, and unexpected events can make…

It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of…

The classical motion of a one-dimensional chain of atoms coupled through a specific force function that depends on position shows features very similar to the Wannier-Stark problem of a quantum particle under the combined effects of a…

Many modern applications of the artificial neural networks ensue large number of layers making traditional digital implementations increasingly complex. Optical neural networks offer parallel processing at high bandwidth, but have the…

Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted,…

Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit.…

Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…

Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this approach is the identification and utilization…