Transmission Properties of the One-Dimensional Array of Delta Potentials

Abstract

The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the transmission probability of the particle. Results for arbitrary N and for specific regular arrays are presented. Some particular symmetries and invariances of the delta-function potential array for the N = 2 case are analyzed in detail. It is shown that perfect transmission can take place in a variety of situations.

Recurrence in Resonant Transmission of One-Dimensional Array of Delta Potentials

“…Otherwise we can expect maximal values in the transmitivitty but not perfect tunnelling. Considering the cells as potential barriers, the arbitrary separation between the two cells (in the example 150 nm) can create resonances for different incident energies, but never perfect tunnelling, unless the two cells are equal, as it was shown in [39].…”

“…From this result, it is easy to see that if the two δ-function potential have the same strength (λ 1 = λ 2 = λ), then for E 2 E 1 = −z/z * one obtains T = 1 for any λ (for graphical representation and other details see [39]). This can also be expressed as…”

“…In our previous work [39], some specific regular arrays were considered. Here we note that E n = exp(2ikx n ) is the square of the wave function at x = x n for particle travelling to the right.…”

“…This paper is organized as follows. In order to clarify the results and discussion, in the section 2 we give the transfer matrix method and its representation which was given recently [39]. In section 3 we present the conditions for resonant transmission and perfect tunnelling for arrays with N = 2, 3 and 4.…”

Entanglement of magnetic impurities through electron scattering in an electric field

“…An alternative initial state with the anti-parallel impurity spins (|↑ 1 and |↓ 2 or |↓ 1 and |↑ 2 ) add an extra asymmetry in the system. Although this asymmetry does not eliminate all the resonant effects, it restricts the constructive quantum interference [34]. It also affects the indistinguishability of the Feynmann paths of the scattered electron, decreasing the level of entanglement created [26,25].…”