Transport properties through graphene with sequence of alternative magnetic barriers and wells in the presence of time-periodic scalar potential

We investigate the electronic transport properties of a graphene sheet under the magnetic barriers and wells through the oscillating scalar potential combined with the static scalar potential barrier having two types of uniform and alternative profiles. We compute the total sideband transmission of the system by additional sidebands at energy, in presence of oscillating potential, $$V_1$$ V 1 , using the transfer-matrix formalism and the Floquet sidebands series. The oscillating potential, generally, suppresses the Klein tunneling and the confinement of the charge carriers. In the absence of $$V_1$$ V 1 , both profiles show the wave vector filtering effect for the carriers by controlling the energy E relative to the potential barrier height, $$V_0$$ V 0 . The $$(N-1)$$ ( N - 1 ) -fold resonance splittings are observed through a region around $$E=V_0$$ E = V 0 with reduction of the transmission. The transmission vanishes in this region upon increasing the number of magnetic blocks N, strength of the magnetic field B in both configurations. We present an estimate relation for the width of the reduction region expressed in terms of E, $$V_0$$ V 0 , B and the angle of incidence of the quasiparticles. We observe, in the second profile, $$(N-1)$$ ( N - 1 ) -fold resonances in the transmission for special values of $$E=V_0$$ E = V 0 with a separation depending on the width of the magnetic blocks. The magnetic field and the width of the magnetic blocks have critical values, where the transmission reduces to zero. All the features observed in the transmission reflect to the conductance. In both configurations, there are some peaks in the conductance corresponding to the resonances of the transmission. The oscillations of the conductance are obtained which was observed in the experimental results. We, also, find the possibility for switching the transport properties of the system by changing the characteristic parameters of the magnetic system.

Quantum Dynamics: Resonance and a Quantum Flip-Flop

This chapter begins the discussion of the time evolution of an active quantum system. From the earlier chapters, time dependent physics has been observed through the presence of the time evolution of the phase of each eigenstate. The Hamiltonian itself is time independent. This represents the same kind of evolution of a classical system like the vibration of a tuning fork when it has been struck or the oscillation of an LC circuit if the capacitor is charged to some voltage and then the switch is closed. In the quantum case, the Hamiltonian has also been time independent. The time evolution evolves according the full-time dependent Schrödinger equation, depending only on a single initial condition of the state vector or wave function and the corresponding time evolution of the phase factor for each eigenstate. However in this chapter, we consider the case of when there is a time dependent Hamiltonian such as a sinewave generator or laser. As in the case of resonant tunneling, we see the importance in dynamics of resonant coupling. With an oscillating potential energy term, we see the presence of Rabi oscillations in the probability amplitude of a two-state system on resonance, which can be viewed as a quantum flip-flop between two states of a quantum bit (qubit).

Quenching effect of oscillating potential on anisotropic resonant transmission through a phosphorene electrostatic barrier

The anisotropy in resonant tunneling transport through an electrostatic barrier in monolayer black phosphorus either in presence or in absence of an oscillating potential is studied. Non-perturbative Floquet theory is applied to solve the time dependent problem and the results obtained are discussed thoroughly. The resonance spectra in field free transmission are Lorentzian in nature although the width of the resonance for the barrier along the zigzag (Г–Y) direction is too thinner than that for the armchair (Г–X) one. Resonant transmission is suppressed for both the cases by the application of oscillating potential that produces small oscillations in the transmission around the resonant energy particularly at low frequency range. Sharp asymmetric Fano resonances are noted in the transmission spectrum along the armchair direction while a distinct line shape resonance is noted for the zigzag direction at higher frequency of the oscillating potential. Even after the angular average, the conductance along the Г–X direction retains the characteristic Fano features that could be observed experimentally. The present results are supposed to suggest that the phosphorene electrostatic barrier could be used successfully as switching devices and nano detectors.

Two-scale homogenization of a stationary mean-field game

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.