Single Band Motion of Conduction Electrons in a Uniform Magnetic Field

The Weyl Representation on the Torus

“…Indeed, to apply this semiclassical limit we must evaluate the integrals in (5.14) by the stationary phase approximation as in [1], so 17) where M is the symplectic matrix for the linearized transformation between the neighborhood of the tips of the chord ξ(x) generated by S t (x) as a center function.The index runs over all the contributing classical orbits. In the case of a single orbit, the corresponding Morse index µ j = 0.…”

PT symmetric Aubry–Andre model

“…Apparently, the non-Hermitian character of the AubryAndre equation (1) could change the physics of this system dramatically. Note also that Aubry-Andre model coincides with the Harper model when V = 2 and γ 0 = 0 and the energy spectrum as a function of β is known as Hofstadter butterfly spectrum, which is an example of fractal structure that appears in physics [26,27]. Here, we study the Hofstadter butterfly spectrum and localization effect for the PT symmetric Aubry-Andre model.…”

“…Our system is described by the PT symmetric extension of the Aubry Andre model [25]. The energy spectrum associated with Hermitian Aubry-Andre model at certain strength of parameters has fractal structure, which is known as the Hofstadter butterfly spectrum [26,27]. We also investigate the Hofstadter butterfly spectrum in the presence of nonHermitian impurities.…”

Interactions propel a magnetic dance

“…Compared with healthy individuals, people who have an impaired type I interferon response can be prone to infections, whereas individuals who have an overactive response might have autoimmune disease or organ damage associated with inflammation 3,4 . Abnormal activation of the type I interferon response is observed in most people with lupus, and a clinical study 5 found that interferon-related gene expression correlates with specific disease features.…”