On the Boltzmann equation with the symmetric stable Levy process

As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the stochastic time-evolution of characteristic functions associated with the symmetric stable Levy process and the Maxwellian collision dynamics. Under a non-cutoff assumption on the kernel, we establish a global existence theorem with maximum growth estimate, uniqueness and stability of solutions.Comment: in Kinetic and Related Models, 201

Local Existence for the Spatially Homogeneous Boltzmann Equation with Soft Potentials

We prove a local-in-time existence and uniqueness theorem for a smooth classical solution to the spatially homogeneous Boltzmann equation with cutoff soft potentials. Our proof is based on a series of bilinear estimates for the integrability and Sobolev regularity of the associated collision operator. While the global-in-time existence is left inconclusive, we give a lower bound of the maximal time of existence and a necessary condition for finite time extinction of existence.Comment: in Kinetic and Related Models, 201

Absolute moments and Fourier-based probability metrics

We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary order, we exploit our formulae to characterize its Fourier image and construct Fourier-based probability metrics which make the space complete. As applications, we compute absolute moments of those probability measures whose characteristic functions belong to the Scheonberg classes, estimate absolute moments of convolutions and investigate the asymptotic behavior of solutions to the heat-diffusion equations from a probability view-point

Real-space Hamiltonian method for low-dimensional semiconductor heterostructures

We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is extremely simple; all subband energy levels and envelope functions are directly obtained by a single evaluation of the heterostructure Hamiltonian matrix. We test the method in the 6- and 8-band k \cdot p models as well as in a simple parabolic one-band model and demonstrate its great accuracy. The method can be straightforwardly generalized to a general n-band k \cdot p model. We describe three different approaches within the method which make it possible to investigate the origin and removal of the spurious or unphysical solutions, which has long been an important issue in the community.Comment: 44 pages, 15 figure

Newton diagram of positivity for 1F2{}_1F_2 generalized hypergeometric functions

As for the positivity of ${}_1F_2$ generalized hypergeometric functions, we present a list of necessary and sufficient conditions in terms of parameters and determine the region of positivity by certain Newton diagram.Comment: 19 pages, 3 figure

Locality of the overlap-Dirac operator on topology-fixed gauge configurations

We investigate the locality property of the overlap-Dirac operator on gauge configurations generated with extra Wilson fermions. By such extra terms we expect that the structure of the Aoki phase would change drastically. In particular, we study the possibility of defining the overlap-Dirac operator in the strong coupling regime keeping its exponential locality.Comment: 7 pages, 5 figures, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi

Morse theory in path space

We consider the path space of a curved manifold on which a point particle is introduced in a conservative physical system with constant total energy to formulate its action functional and geodesic equation together with breaks on the path. The second variation of the action functional is exploited to yield the geodesic deviation equation and to discuss the Jacobi fields on the curved manifold. We investigate the topology of the path space using the action functional on it and its physical meaning by defining the gradient of the action functional, the space of bounded flow energy solutions and the moduli space associated with the critical points of the action functional. We also consider the particle motion on the $n$-sphere $S^{n}$ in the conservative physical system to discuss explicitly the moduli space of the path space and the corresponding homology groups.Comment: 6 page

Dynamics of stringy congruence in early universe

We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. In this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and the shear in terms of the expansion of the universe. In appendix we investigate the geodesic surface congruence of the null strings.Comment: 11 page

Spin-polarized bandgap of graphene induced by alternative chemisorption with MgO (111) substrate

Using First-principle calculations, substrate effect of O-terminated (rt3 x rt3) MgO (111) on graphene was investigated for spintronics application. Surprisingly, the graphene can be turned into a spin-polarized semiconductor, which implies that the totally spin-polarized current can be generated and its on/off switching can be also controlled. The origin of the spin-polarized band structure is spin-ordering due to alternative sp2-sp3 covalent bondings induced by the MgO (111) substrate. The results indicate that the tailored pattern of the chemisorption can be highly efficient or introducing totally spin-polarized current to the graphene.Comment: This paper has been withdrawn due to a crucial typo in the Figure

String reveals secrets of universe

Stringy cosmology displays features that are different from standard cosmology. One may be surprised in that in this scenario there is no phase transition between the radiation dominated phase and matter dominated phase and the universe is cyclic similar to brane cyclic cosmology.Comment: 2 page