Analysis of lense‐governed Wigner signed particle quantum dynamics

Abstract

We present a Wigner signed particles analysis of the lense‐governed electron state dynamics based on the quantitative theory of coherence reformulated in phase space terms. Electrostatic lenses are used for manipulating electron evolution and are therefore attractive for applications in novel engineering disciplines like entangletronics. The signed particle model of Wigner evolution enables physically intuitive insights into the processes maintaining coherence. Both, coherent processes and scattering‐caused transitions to classical dynamics are unified by a scattering‐aware particle model of the lense‐controlled state evolution. Our approach bridges the fairly new theory of coherence with the Wigner signed particle method.

Investigating Quantum Coherence by Negative Excursions of the Wigner Quasi-Distribution

“…The map establishes a one-to one correspondence between operators and functions, or more precisely an isomorphism from the algebra of operators  (xp) with a product and a commutator [,] to the algebra of phase space functions A(x, p) with a non-commutative star ( * )-product A * B = W( •B) and a Moyal bracket ih[A, B] M = W  ,B . Recently, the algebraic notions used to derive the quantifying theory of coherence have been reformulated in terms of the Wigner theory [20].…”

“…We conclude that incoherent states involve only diagonal elements f ii : From Equation (2) it follows that coherence is directly related to the existence of nondiagonal elements f ij in the state representation of f w . The above formal mathematical analysis developed in [20] can be directly linked to the negativity of the Wigner function and actually has a transparent physical background in terms of positive and negative particles. Indeed, if we choose  to be the momentum operator  =p with a basis e i pj x/h , the corresponding Wigner basis becomes…”

Electron Interference in a Double‐Dopant Potential Structure

“…In this work the term entanglement is thus understood to represent the complicated coupling between device and contact states. It further covers the term entangletronics, short for entangled electronics, and extends it over a much broader class of problems beyond the strict meaning of quantum entanglement. Therefore, entangletronics is understood to rely on mechanisms which maintain coherence, while the environment strives to destroy it.…”

“…In a previous communication we showed that the Wigner formalism provides a legitimate theoretical framework for presenting the basic notions of the quantification theory of coherence in phase space terms . Based on the resulting criteria for coherence in phase space in conjunction with a Wigner signed particle approach, we demonstrated that a quantum state can be split and controlled by an electrostatic lense and how the environment kills the coherence.…”

“…Concerning transport properties, we assume ballistic transport, which in terms of wave mechanics relates to coherent transport: In the used quantum transport model (used for simulating nanoelectronic devices), coherence is destroyed by any process which influences the free movement of the signed particles, for example, phonon scattering. Although the theory and the simulation framework support phonon scattering, here our focus is on clearly highlighting the manifesting quantum effects. This requires a maximum resolution of the results, in turn requiring that all phonon scattering effects are suppressed.…”