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By Michael V Moskalets
The purpose of this e-book is to introduce the elemental parts of the scattering matrix method of shipping phenomena in dynamical quantum platforms of non-interacting electrons. This strategy admits a bodily transparent and obvious description of shipping approaches in dynamical mesoscopic platforms promising simple components of solid-state units for quantum details processing. one of many key results, the quantum pump impression, is taken into account intimately. furthermore, the speculation for a lately carried out new dynamical resource -- injecting electrons with time hold up a lot higher than the electron coherence time -- is available. This thought presents an easy description of quantum circuits with one of these single-particle resource and indicates in an unambiguous approach that the tunability inherent to the dynamical structures results in a couple of unforeseen yet primary results.
Readership: Physicists, chemists and electric engineers who're attracted to non-stationary delivery phenomena in quantum platforms.
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Extra resources for Scattering Matrix Approach to Non-Stationary Quantum Transport
Example text
NL +1 α=1 Therefore, we have TLR (−H) = TRL (H) . 77) Combining together Eqs. 77) we finally arrive at the required relation TLR = TRL TLR (−H) = TRL (H) ⇒ TLR (H) = TLR (−H), which shows that the conductance, G = G0 TLR , of a sample with two quasi-one-dimensional leads is an even function of a magnetic field. July 28, 2011 15:17 28 World Scientific Book - 9in x 6in moskalets-ws-book9x6 Scattering matrix approach to non-stationary quantum transport µ3 I3 = 0 µ1 = µ0 + eV1 Fig. 5 µ2 = µ0 + eV2 A mesoscopic scatterer with current carrying (1 , 2) and potential (3) leads.
56), which results in linear I–V characteristics, Eq. 53). On the other hand if one cannot ignore the energy dependence of Sαβ (E) then the current becomes a non-linear function of a bias. As a simple example we consider a sample with two leads (α = 1, 2) whose scattering properties are governed by the resonance level of a width Γ located at the energy E1 : 2 |S12 (E)| = Γ2 . 57) For simplicity suppose that E1 = µ0 . Then substituting the equation above into Eq. 56) we find a current { ( ) ( )} e eV2 eV1 I1 = Γ arctan − arctan .
87), gives Re e−ikL /t = 1. Then [ ( )]2 at ϕ = 0 we find from Eq. 86a), Im e−ikL /t = R/T . Therefore, [ ( −ikL )]2 2 |F | = T Im e /t /R = T R/(T R) = 1. , ϕ = ̸ 0), then )the ( −ikL current is not zero. 87), Re e /t = cos(ϕ), we calculate |F |2 [ ( −ikL )]2 ( −ikL ) e e R |F |2 = Im sin(ϕ) . 86) we find [ ( Im e−ikL t )]2 = sin2 (ϕ) + R . T Substituting the equation above into Eq. 92) and then into Eq. 91) we calculate the current I=− e k mL T sin(ϕ) T sin(ϕ) + R sin(ϕ) − Im . 93) ) If we denote t = it0 eiχ then the dispersion equation gives: sin(kL + χ) = −t0 cos(ϕ).