Vanishing or non-vanishing rainbow? Reduction formulas of electric dipole moment

In this paper, we derive a simplified formula of electric dipole moments (EDMs) of a fermion. In the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by W boson exchanges occur in the calculation of the neutron EDM at the two-loop level due to the gauge symmetry. The fermion self-energy and the vertex correction are related through the Ward-Takahashi identity, and this relation causes the exact cancellation of the EDM. We derive EDM formulas for a more general setup by introducing the form factors for the fermion self-energy and the vertex correction so that the derived formulas can be applicable to a larger class of models. We conclude that the non-zero EDM contributions are induced from rainbow-type diagrams with the chirality flipping effects for internal fermions. We also discuss the other possible generalization of the EDM calculation which is applicable to the other classes of models.

Full electric-field tuning of the nonreciprocal transport effect in massive chiral fermions with trigonal warping

In a noncentrosymmetric system, an intrinsic electric polarization is allowed and may lead to unusual nonreciprocal charge transport phenomena. As a result, a current-dependent resistance, arising from the magnetoelectric anisotropy term of k · E × B, appears and acts as a current rectifier with the amount of rectification being linearly proportional to the magnitude of both current and applied magnetic field. In this work, a different type of nonreciprocal transport effect was demonstrated in a graphene-based device, which requires no external magnetic field. Owing to the unique pseudospin (valley) degree of freedom in chiral fermions with trigonal warping, a large nonreciprocal transport effect was uncovered in a gapped bilayer graphene, where electric-field tunabilities of the band gap and valley polarization play an important role. The exact cancellation of nonreciprocal effect between two different valleys is effectively removed by breaking the inversion symmetry via electric gatings. The magnitude of the current rectification appears to be at a maximum when the Fermi surface undergoes a Lifshitz transition near the band edges, which is proportional to the current and the displacement field strength. The full electric-field tuning of the nonreciprocal transport effect without a magnetic field opens up a new direction for valleytronics in two-dimensional based devices.

Theory of Nonsinusoidal Small Antennas with Applications to Near-Field Communication System Analysis and Design

We provide a conceptual and theoretical analysis of nonsinusoidal antennas with emphasis on how electromagnetics and communication theories can be integrated to propose ideas for near-field (NF) communications systems utilizing future antennas. It is shown through rigorous analysis that in nonsinusoidal antennas it is possible to derive and solve ordinary differential equations giving specialized time-domain excitation signals that lead to exact cancellation of the near field at specific radiation spheres. This opens the door to building NF communications systems with far-field-like communication receiver infrastructures utilized if the receive antenna is placed at the special sphere where the NF component is made to vanish.

Theory of Nonsinusoidal Small Antennas with Applications to Near-Field Communication System Analysis and Design

We provide a conceptual and theoretical analysis of nonsinusoidal antennas with emphasis on how electromagnetics and communication theories can be integrated to propose ideas for near-field (NF) communications systems utilizing future antennas. It is shown through rigorous analysis that in nonsinusoidal antennas it is possible to derive and solve ordinary differential equations giving specialized time-domain excitation signals that lead to exact cancellation of the near field at specific radiation spheres. This opens the door to building NF communications systems with far-field-like communication receiver infrastructures utilized if the receive antenna is placed at the special sphere where the NF component is made to vanish.

On high-order perturbation expansion for the study of long–short wave interactions

In high-order analysis and simulation of long–short surface wave interaction using mode decomposition, ‘divergent’ terms of the form $k_{S}a_{L}=O(\unicode[STIX]{x1D6FE}\unicode[STIX]{x1D716})\gg 1$ appear in the high-order expansions, where $k_{L,S}$, $a_{L,S}$ are respectively the long, short modal wavenumbers and amplitudes, with $\unicode[STIX]{x1D6FE}\equiv k_{S}/k_{L}\gg 1$ and $k_{L}a_{L}\sim k_{S}a_{S}=O(\unicode[STIX]{x1D716})$ finite. We address the effect of these terms on the numerical scheme, showing numerical cancellation at all orders $m$; but increasing ill-conditioning of the numerics with $\unicode[STIX]{x1D6FE}$ and $m$, which we quantify. In the context of mode decomposition, we show theoretical exact cancellation of the divergent terms up to $m=3$, extending the existing result of Brueckner & West (J. Fluid Mech., vol. 196, 1988, pp. 585–592) and supporting the conjecture that this is obtained for all orders $m$. We show the latter by developing a theoretical proof for any $m$ using a Dirichlet–Neumann operator and mathematical induction. The implication of the theoretical proof on the numerical simulation of long–short wave interaction is discussed.

Quantum Kinetic Equations

The gradient approximations of the Kadanoff and Baym equations are derived up to first order. The off-shell motions responsible for the satellites are shown to ensure causality. The cancellation of off-shell motions from the drift and correlation part of the reduced density provides a precursor of the kinetic equation for the quasiparticle distribution which leads to a functional between reduced and quasiparticle distribution, named the extended quasiparticle picture. Virial corrections appear as internal gradients in the selfenergy and therefore in the considered processes. With this extended quasiparticle picture, the non-Markovian kinetic equations are transformed into Markovian ones for proper defined quasiparticles without neglect showing the exact cancellation of off-shell parts. Alternative approaches are discussed for comparison.

Collisions of two breathers at the surface of deep water

We present results of numerical experiments on long-term evolution and collisions of breathers (which correspond to envelope solitons in the NLSE approximation) at the surface of deep ideal fluid. The collisions happen to be nonelastic. In the numerical experiment it can be observed only after many acts of interactions. This supports the hypothesis of "deep water nonintegrability". The experiments were performed in the framework of the new and refined version of the Zakharov equation free of nonessential terms in the quartic Hamiltonian. Simplification is possible due to exact cancellation of nonelastic four-wave interaction.

Collisions of two breathers at the surface of deep water

We present results of numerical experiments on long time evolution and collisions of breathers (which correspond to envelope solitons in the NLSE approximation) at the surface of deep ideal fluid. The collision happens to be nonelastic. In the numerical experiment it can be observed only after many acts of interactions. This supports the hypothesis of "deep water nonintegrability". The experiments were performed in the framework of the new and refined version of the Zakharov equation free of nonessential terms in the quartic Hamiltonian. Simplification is possible due to exact cancellation of nonelastic four-wave interaction.