We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel–Killing and Killing–Yano tensors is pointed out. Some nontrivial examples involving Runge–Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of t...

polycyclic aromatic hydrocarbons (pahs) are a class of compounds consisting of more than twobenzene rings fused in a linear, angular, or clustered arrangement and do not contain hetero atomsor carry subsistent. pahs originate from various sources. they are primarily formed byincomplete combustion of carbon-containing fuels such as wood, coal, diesel, fat, or tobacco. thepresent study reports an...

Three-dimensional Hopf insulators are a class of topological phases beyond the tenfold-way classification. At critical point transition between two distinct with rotational symmetry, band-touching points Berry dipoles opposite charges overlapping in mirror-symmetric way, and carry unique curvature structures leading to special quantization flux. Close such Berry-dipole transitions, we find that...

We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N -way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and “matricization.” We have further added two classes for representing tensors in decomposed format: cp tensor and tucker tensor. We demonstrate the use o...