Mathematics

  2010 MAR 9 - (VerticalNews.com) -- According to recent research from Frascati, Italy, "Quantum interference effects in rings provide suitable means for controlling spin at mesoscopic scales. Here we apply such a control mechanism to the spin dependent transport in a one-dimensional Aharonov-Bohm (AB) ring patterned in two-dimensional electron gases (2DEGs) symmetrically coupled to two leads."

  "We investigate the ballistic conductance in the presence of an artificial crystal, which is made up of 5 quantum dots. The study is essentially based on the natural spinorbit interactions, due to the quantum well potential that confines electrons in the 2DEG. We focus on single-channel transport and solve for the spin polarization of the current. As an important consequence of the presence of spin splitting, we find the occurrence of spin dependent current oscillations. The presence of lattice can be useful to improve the spin filtering capability of the QR. In fact modulating both the geometry of the dots and the strength of the tunnel barriers between them it is now possible to obtain well defined spin-dependent resonances allowing polarized transport," wrote S. Bellucci and colleagues ...read more

  2010 MAR 9 - (VerticalNews.com) -- According to a study from Dhahran, Saudi Arabia, "A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schrodinger equation in terms of square integrable basis. The main characteristic of the basis is that it supports an infinite tridiagonal matrix representation of the wave operator."

  "However, the eigenenergies associated with this potential cannot be obtained using traditional procedures. Hence, a new approach (the 'potential parameter' approach) has been adopted for this eigenvalue problem. For a fixed energy, the problem is solvable for a set of values of the potential parameters (the 'parameter spectrum'). Subsequently, the map that associates the parameter spectrum with the energy is inverted to give the energy spectrum," wrote H. Bahlouli and colleagues ...read more

  2010 MAR 9 - (VerticalNews.com) -- "A principled framework to generalize variational perturbation approximations (VPAs) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free energy (GFE) with a variational procedure formulated using q-deformed calculus," scientists writing in the journal Physica a - Statistical Mechanics and Its Applications report ...read more