Comparing two different descriptions of the I-V characteristic of graphene: theory and experiment

The formalism of the nonperturbative description of transport phenomena in graphene on the framework of the quantum kinetic equation for the Schwinger-like process is compared with the description on the basis of Zener-Klein tunneling. The regime of ballistic conductivity in a constant electric field is considered. In the latter case the interaction of carriers with electric field is described in terms of the spatial dependence of their potential energy (x-representation). The presented kinetic formalism uses an alternative method of describing the interaction with a field through the introduction of a quasimomentum $P=p-(e/c)A(t)$ where $A(t)$ is the vector potential (t-representation). Both approaches should lead to the same physical characteristics of the described process. The measurement of the current in experiments is realized in static conditions determined by the potential difference between the electrodes and the distance between them. These parameters are native for the x-representation. On the contrary, in the approach based on the t-representation it is necessary to consider the situation in dynamics and introduce the effective lifetime of the generated carriers. In the ballistic regime this time depends on the distance between the electrodes. We give a detailed comparison of these two descriptions of the current and demonstrate good coincidence with the experimental data of the alternative approach based on the t-representation. It provides a reliable foundation for the application of nonperturbative methods adopted from strong field QED, that allows to include in the consideration more general models of the field (arbitrary polarization and time dependence) and to extend the scope of the theory.Comment: 7 pages, 3 figures, accepted for publication in EPJ Web of Conf. as contribution to the Proceedings of the XXIV International Baldin Seminar on High Energy Physics Problems, Dubna, Russia, September 17-22, 201

Three-photon states in nonlinear crystal superlattices

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: $\omega_{0}\rightarrow\omega_{1}+\omega_{2}$, $\omega_{2}\rightarrow\omega_{1}+\omega_{1}$ under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.Comment: 15 pages, 6 figure

Assessment of the differential entropy of random vectors

Hereby, the features of assessment of differential realization of random vectors for practical use are considered. The question of the stability of the assessment procedure for the presence of anomalous observations in the samples was investigated. The possibility of using differential entropy for samples of random vectors is considered, some components of which are presented in grouped form as discrete quantities. Examples are given of differential entropy assessment with the help of the proposed algorithms.Рассмотрены особенности оценивания дифференциальной реализации случайных векторов для практического использования. Исследован вопрос устойчивости процедуры оценивания к присутствию в выборках аномальных наблюдений. Рассмотрена возможность использования дифференциальной энтропии для выборок случайных векторов, некоторые компоненты которых представлены в сгруппированном виде как дискретные величины. Приведены примеры оценивания дифференциальной энтропии с помощью предложенных алгоритмов.Исследование выполнено при поддержке РФФИ, грант № 17-01-00315а