For the periodic sphaleron potential in the electroweak theory, we find the one-dimensional time-independent Schr{o}dinger equation with the Chern-Simons number as the coordinate, construct the Bloch wave function and determine the corresponding cond
ucting (pass) band structure. We show that the baryon-lepton number violating processes can take place without the exponential tunneling suppression (at zero temperature) at energies around and above the barrier height (sphaleron energy) at 9.0 TeV. Phenomenologically, probable detection of such processes at LHC is discussed.
Recent BICEP2 detection of low-multipole B-mode polarization anisotropy in the cosmic microwave background radiation supports the inflationary universe scenario and suggests a large inflaton field range. The latter feature can be achieved with axion
fields in the framework of string theory. We present such a helical model which naturally becomes a model with a single cosine potential, and which in turn reduces to the (quadratic) chaotic inflation model in the super-Planckian limit. The slightly smaller tensor/scalar ratio $r$ of models of this type provides a signature of the periodic nature of an axion potential. We present a simple way to quantify this distinctive feature. As axions are intimately related to strings/vortices and strings are ubiquitous in string theory, we explore the possibility that cosmic strings may be contributing to the B-mode polarization anisotropy observed.
This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely determined for a gi
ven total number of vehicles on the ring road. The solution is exact and always stable with respect to the first-order continuum model, whereas it is a good approximation with respect to the semi-discrete model provided that the involved equilibrium constant states are linearly stable. In an otherwise case, the instability of one or more equilibria could trigger stop-and-go waves propagating in certain road sections or throughout the ring road. The indicated results are reasonable and thus physically significant for a better understanding of real traffic flow on an inhomogeneous road.
We study a racetrack model in the presence of the leading alpha-correction in flux compactification in Type IIB string theory, for the purpose of getting conceivable de-Sitter vacua in the large compactified volume approximation. Unlike the Kahler Up
lift model studied previously, the alpha-correction is more controllable for the meta-stable de-Sitter vacua in the racetrack case since the constraint on the compactified volume size is very much relaxed. We find that the vacuum energy density Lambda for de-Sitter vacua approaches zero exponentially as the volume grows. We also analyze properties of the probability distribution of Lambda in this class of models. As in other cases studied earlier, the probability distribution again peaks sharply at Lambda=0. We also study the Racetrack Kahler Uplift model in the Swiss-Cheese type model.
