On the tunneling through a time dependent barrier

Tunneling of a nucleon through a monotonically shrinking rectangular barrier is solved exactly. Some consequences for the nucleon-transfer in the approach phase of two colliding heavy nuclei are discussed.     

Nonlinear tunneling through a strong rectangular barrier

Nonlinear tunneling is investigated by analytically solving the one-dimensional Gross–Pitaevskii equation(GPE)with a strong rectangular potential barrier. With the help of analytical solutions of the GPE, which can be reduced to the solution of the linear case, we find that only the supersonic solution in the downstream has a linear counterpart. A critical nonlinearity is explored as an up limit, above which no nonlinear tunneling solution exists. Furthermore, the density solution of the critical nonlinearity as a function of the position has a step-like structure.     

Features of the tunneling of a system with an internal degree of freedom through a potential barrier

The tunneling of a quantum system with an internal degree of freedom through a potential barrier is considered. Based on the exact numerical solution to the nonstationary Schrödinger equation, the tunneling of a model two-particle system through a potential barrier is studied and the dependences of the tunneling transparency of the barrier on the parameters of the wave packet that describes the system at the initial moment are obtained. A sharp increase in the tunneling probability related to the formation of a long-lived quasibound state of the system in the barrier region is demonstrated. A simple analytical model of the tunneling of a system with an internal degree of freedom that allows for a qualitative interpretation of the main features of the tunneling is constructed.     

Dissipative tunneling through a parabolic potential in the Lindblad theory of open quantum systems

By using the Lindblad theory for open quantum systems, an analytical expression of the tunneling probability through an inverted parabola is obtained. This penetration probability depends on the environment coefficients. It is shown that the tunneling probability increases with the dissipation and the temperature of the thermal bath. Received 15 October 1999 and Received in final form 5 January 2000     

Tunneling through a disordered potential barrier

Tunnelling through a weakly disordered potential barrier is studied analytically. A perturbative approach is developed to calculate all statistical moments of the tunnelling transmission coefficient, and its probability distribution function. It is shown that on average disorder enhances the tunnelling conductance, resistance, and the coherent component of the transmitted field.On leave from the Institute of Low-Temperature Physics and Engineering, Kharkov 310164, Ukraine.     

Complete tunneling of light through a barrier with anisotropic metamaterial

We construct a barrier with anisotropic metamaterial to explore the complete tunneling conditions of light through it. And then we take a semiconductor metamaterial as an example to discuss the dispersive properties of the barrier and show a possible application as a flat-top filter.     

Quasiparticle tunneling through a barrier in the fractional quantum hall regime

Tunneling of fractionally charged quasiparticles (QPs) through a barrier is considered in the context of a multiply connected geometry. In this geometry global constraints do not prohibit such a tunneling process. The tunneling amplitude is evaluated and the crossover from mesoscopic QP-dominated to electron-dominated tunneling as the system's size is increased is found. The presence of disorder enhances both electron and QP-tunneling rates.     

Particle tunneling and scattering in a three-dimensional potential with a barrier

The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.      

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Electron tunneling through a barrier that depends linearly on time

We discuss the creation of a negative molecular ion via the decay of a self-captured electron state — the fluctuon — in a nonideal dipole-molecule gas. The creation probability of the negative ion is evaluated in the classical approximation using Green's function methods. We assume that the potential barrier through which the electron tunnels from the potential well of the fluctuon to that of the molecule depends linearly on time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 84–88, September, 1987.     

Tunneling time of electrons through a potential barrier

We investigate the problem of the average time spent by a tunneling electron in the classically forbidden region. We propose a natural method of generalizing the classical transit time concept to the quantum mechanical case and apply it to the problem of tunneling through a one-dimensional potential barrier. Considering the transmitted and reflected particles separately yields complex parameters which represent the tunneling times of reflected and transmitted particles. We investigate the connection of these parameters to the angles of rotation of electron spins in a magnetic field localized in the barrier region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 26–29, March, 1987.     

Electron tunneling through thin barrier with smooth potential at GaAs/AlAs(001) heterointerfaces

The influence of actual microscopic potential on the characteristics of resonant electron tunneling from the Γ valley in GaAs through the AlAs barrier with thickness of one lattice constant has been investigated by the methods of pseudopotential and scattering matrix factorized by the irreducible representations of the symmetry group of the heterostructure. The transition regions between the potentials of components and the barrier region are treated as the components of the Ga₂Al₂As₄ superlattice spacing to provide the continuity of the crystal potential at the boundaries of the matching of wave functions. It is demonstrated that, compared to the results obtained in the abrupt-interface model, the inclusion of the actual potential in the calculation leads to changes in the number and location of the Fano resonances, an enhancement in the localization of electron density within the barrier, and a drastic increase in the tunneling time.     

Experimental barrier heights and the image potential in scanning tunneling microscopy

The effect of the classical image potential on the tunnel-barrier heights deduced from scanning tunneling microscopy is considered. An earlier prediction that the image potential should lead to an observable difference in barrier heights as deduced from two different measurements is shown to be incorrect. Using an approximation to the full multiple image potential we find that the barrier height deduced from the variation of current with tunnel-barrier width is extremely close to the unreduced work function, and we discuss what characteristic of the image potential leads to this result.     

Anomalously long passage through a rounded-off-step potential due to a new mechanism of multidimensional tunneling

The fully complex domain semiclassical theory based upon the complexified stable-unstable manifold theory, which we have developed in our recent studies, is successfully applied to explain anomalous tunneling phenomena numerically observed in a periodically modulated round-off-step potential. Numerical experiments show that tunneling through the oscillating step potential is characterized by a spatially nondecaying tunneling tail and an anomalously slow relaxation. The key is the existence of a critical trajectory exhibiting singular behavior, and the analysis of neighboring trajectories around it reproduces the essence of such anomalous phenomena.