While the Sauter-Schwinger effect describes nonperturbative electron-positron pair creation from vacuum by a strong and slowly varying electric field Estrong via tunneling, the dynamically assisted Sauter-Schwinger effect corresponds to a strong (exponential) enhancement of the pair-creation probability by an additional weak and fast electric or electromagnetic pulse E weak . Using the WKB and worldline instanton method, we find that this enhancement mechanism strongly depends on the shape of the fast pulse. For the Sauter profile 1/ cosh 2 (ωt) considered previously, the threshold frequency ωcrit (where the enhancement mechanism sets in) is basically independent of the magnitude E weak of the weak pulse-whereas for a Gaussian pulse exp(−ω 2 t 2 ), an oscillating profile cos(ωt) or a standing wave cos(ωt) cos(kx), the value of ωcrit does depend (logarithmically) on E weak /Estrong.

In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: (a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function (NEGF) method to the tight-binding model with local strain, (b) the general relativistic approach in which classical trajectories of relativistic point particles moving in a curved surface with a pseudo-magnetic field are calculated. The connection between the two is established in the long-wave limit via an effective Dirac Hamiltonian in curved space. Geometrical optics approximation, applied to focused current beams, allows us to directly compare the wave and the particle pictures. We obtain very good numerical agreement between the quantum and the classical approaches for a fairly wide set of parameters, improving with the increasing size of the system. The presented method offers an enormous reduction of complexity from irregular tight-binding Hamiltonians defined on large lattices to geometric language for curved continuous surfaces. It facilitates a comfortable and efficient tool for predicting electronic transport properties in graphene nanostructures with complicated geometries. Combination of the curvature and the pseudo-magnetic field paves the way to new interesting transport phenomena such as bending or focusing (lensing) of currents depending on the shape of the deformation. It can be applied in designing ultrasensitive sensors or in nanoelectronics.

The spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of quantum electrodynamics has not yet been confirmed experimentally, as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low-energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter-Schwinger effect. This motivates our proposal for a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.

Elastic deformations of graphene can significantly change the flow paths and valley polarization of the electric currents. We investigate these phenomena in graphene nanoribbons with localized outof-plane deformations by means of tight-binding transport calculations. Such deformations can split the current into two beams of almost completely valley polarized electrons and give rise to a valley voltage. These properties are observed for a fairly wide set of experimentally accessible parameters. We propose a valleytronic nanodevice in which a high polarization of the electrons comes along with a high transmission making the device very efficient. In order to gain a better understanding of these effects, we also treat the system in the continuum limit in which the electronic excitations can be described by the Dirac equation coupled to curvature and a pseudo-magnetic field. Semiclassical trajectories offer then an additional insight into the balance of forces acting on the electrons and provide a convenient tool for predicting the behavior of the current flow paths. The proposed device can also be used for a sensitive measurement of graphene deformations. arXiv:1806.09576v2 [cond-mat.mes-hall]

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.