Spin-current diode with a ferromagnetic semiconductor

Diode is a key device in electronics: the charge current can flow through the device under a forward bias, while almost no current flows under a reverse bias. Here we propose a corresponding device in spintronics: the spin-current diode, in which the forward spin current is large but the reversed one is negligible. We show that the lead/ferromagnetic quantum dot/lead system and the lead/ferromagnetic semiconductor/lead junction can work as spin-current diodes. The spin-current diode, a low dissipation device, may have important applications in spintronics, as the conventional charge-current diode does in electronics.Comment: 5 pages, 3 figure

The spin-polarized ν=0\nu=0 state of graphene: a spin superconductor

We study the spin-polarized $\nu=0$ Landau-level state of graphene. Due to the electron-hole attractive interaction, electrons and holes can bound into pairs. These pairs can then condense into a spin-triplet superfluid ground state: a spin superconductor state. In this state, a gap opens up in the edge bands as well as in the bulk bands, thus it is a charge insulator, but it can carry the spin current without dissipation. These results can well explain the insulating behavior of the spin-polarized $\nu=0$ state in the recent experiments.Comment: 6 pages, 4 figure

Consequences of 't Hooft's Equivalence Class Theory and Symmetry by Large Coarse Graining

According to 't Hooft (Class.Quantum.Grav. 16 (1999), 3263), quantum gravity can be postulated as a dissipative deterministic system, where quantum states at the ``atomic scale''can be understood as equivalence classes of primordial states governed by a dissipative deterministic dynamics law at the ``Planck scale''. In this paper, it is shown that for a quantum system to have an underlying deterministic dissipative dynamics, the time variable should be discrete if the continuity of its temporal evolution is required. Besides, the underlying deterministic theory also imposes restrictions on the energy spectrum of the quantum system. It is also found that quantum symmetry at the ``atomic scale'' can be induced from 't Hooft's Coarse Graining classification of primordial states at the "Planck scale".Comment: 12 papge, Late

Using global invariant manifolds to understand metastability in Burgers equation with small viscosity

The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted $L^2$ space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this "metastable" manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave