Injectance and a Paradox

Abstract

Quantum mechanics manifests in experimental observations in several ways. Hauge et al. (1987) and Leavens et al. (1989) had pointed out that interference effects dominate a physical quantity called injectance. We show that, very paradoxically, the interference related term vanish in a quantum regime making semi-classical formula for injectance exact in this regime. This can have useful implications to experimentalists as semi-classical formulas are much more simple. There are other puzzling facts in this regime like an ensemble of particles can be transmitted without any time delay or negative time delays, whereas the reflected particles are associated with a time delay.

Negative partial density of states in mesoscopic systems

“…We will also show why FSR can become exact whenever there is a phase lapse. This is a physically counter-intuitive result that has been proven for particular potentials so far [10,12,13,15,29]. We will show that this result depends on the properties of Argand diagram and hence very general and independent of the scattering potential.…”

“…In the next section we will argue that this could have been also observed in an experiment. Now let us try to understand if there is a general connection between negative slope and injectance becoming exact as observed in some earlier works [29] for specific potentials. Eq.…”

“…According to the arguments of Leavens and Aers [43], in the semi-classical limit |r 11 | −→ 0 and ρ(1) s = ρ(1) e . But in the cases of studies on injectance or FSR in mesoscopic systems [15,29], |r 11 | = 0 at the energy where ρ(1) s = ρ(1) e , but not very consistently as already discussed in the paragraph after Eq. (26).…”

“…But when the phase drops are gradual like the dashed curve in Fig. 3(c), this has not been proved in general but shown for particular cases [15,29]. Burgers circuit will help us to derive in this work the general connection between gradual phase drops and exactness of semi-classical injectance for any arbitrary potential that can exhibit such a gradual phase drop.…”

Current Delivered by an STM Tip in Landauer-Büttiker Formalism

“…We show that one can obtain the current delivered by an STM tip when brought close to a nano-sized system from the measured scattering phase shift. A number of works have studied FSR and WSDT in the single channel case [4][5][6][7][8][9][10], that relates density of states to scattering phase shift. Another physical quantity related to scattering phase shifts is injectivity or injectance [4] which is the current delivered by an STM tip brought close to a small quantum mechanical system.…”