On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Nucleon Mass Splitting at Finite Isospin Chemical Potential

We investigate nucleon mass splitting at finite isospin chemical potential in the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved that, in the phase with explicit isospin symmetry breaking the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.Comment: 3 pages and no figure

TeV Scale Lee-Wick Fields out of Large Extra Dimensional Gravity

We study the gravitational corrections to the Maxwell, Dirac and Klein-Gorden theories in the large extra dimension model in which the gravitons propagate in the (4+n)-dimensional bulk, while the gauge and matter fields are confined to the four-dimensional world. The corrections to the two-point Green's functions of the gauge and matter fields from the exchanges of virtual Kaluza-Klein gravitons are calculated in the gauge independent background field method. In the framework of effective field theory, we show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a TeV scale Lee-Wick partner of every gauge and matter field as extra degrees of freedom in the theory. Thus the large extra dimension model of gravity provides a natural mechanism to the emergence of these exotic particles which were recently used to construct an extension of the Standard Model.Comment: 17 pages, 3 figures, references added, to appear in Phys. Rev.

Precision measurement of charge number with optomechanically induced transparency

We propose a potentially practical scheme to precisely measure the charge numbers of small charged objects by optomechanical systems using optomechanically induced transparency (OMIT). In contrast to the conventional measurements based on the noise backaction on the optomechanical systems, our scheme makes use of the small deformation of the mechanical resonator sensitive to the charge number of the nearby charged object, which could achieve the detection of a single charge. The relationship between the charge number and the window width of the OMIT is investigated and the feasibility of the scheme is justified by numerical simulation using currently available experimental values.Comment: 6 pages,4 figure

Superstructure-induced splitting of Dirac cones in silicene

Atomic scale engineering of two-dimensional materials could create devices with rich physical and chemical properties. External periodic potentials can enable the manipulation of the electronic band structures of materials. A prototypical system is 3x3-silicene/Ag(111), which has substrate-induced periodic modulations. Recent angle-resolved photoemission spectroscopy measurements revealed six Dirac cone pairs at the Brillouin zone boundary of Ag(111), but their origin remains unclear [Proc. Natl. Acad. Sci. USA 113, 14656 (2016)]. We used linear dichroism angle-resolved photoemission spectroscopy, the tight-binding model, and first-principles calculations to reveal that these Dirac cones mainly derive from the original cones at the K (K') points of free-standing silicene. The Dirac cones of free-standing silicene are split by external periodic potentials that originate from the substrate-overlayer interaction. Our results not only confirm the origin of the Dirac cones in the 3x3-silicene/Ag(111) system, but also provide a powerful route to manipulate the electronic structures of two-dimensional materials.Comment: 6 pages, 3 figure

On effective superpotentials and Kutasov duality

We derive the effective superpotential for an N=1 SU(N_c) gauge theory with one massless adjoint field and N_f massless fundamental flavors and cubic tree-level superpotential for the adjoint field. This is a generalization of the Affleck-Dine-Seiberg superpotential to gauge theories with one massless adjoint matter field. Using Kutasov's generalization of Seiberg duality, we then find the effective superpotential for a related theory with massive fundamental flavors.Comment: 21 pages, Late

Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting