On circuit models for quantum‐classical networks

Abstract

SUMMARYPhysics is not scale invariant, and today the scale of atoms and molecules challenges designers of machines in which quantum effects have dominant sway. What role could circuit theory play in designing machines described by quantum-classical models? Classical equivalent circuits do exist for systems composed of metal contacted and wired devices, such as resonant tunneling diodes, single electron transistors, metalinsulator-metal diodes, etc. circuits, but not for quantum-entangled networks, such as multi-quantum-state atoms.If devices were not contacted and wired by macroscopic metals, i.e. devices were classically field coupled, then generalized circuit models can be introduced. Case studies have been presented on the role of circuit models in quantum-classical systems. However, there are no ideal circuit elements capable of capturing the port properties of quantum-mechanical and/or quantum-optical subsystems and their coupling to classical waveguides or cavities.

A transmission line model for the free electron-positron field

“…The field dynamics is ruled by DIRAC equations, that in the momentum representation and under the assumptions above are written in the form (5) can be grouped in two independent pairs 1 − 3 and 2 − 4. By assuming a solution of the form φ(p, t) =φ(p, 0)e −iEt/ (6) it is seen that each pair admits of the eigenvalues…”

Structural characterization of classical and memristive circuits with purely imaginary eigenvalues

“…[11,13,42,60]). Each qubit is defined by the series connection of a voltage source, a linear capacitor and a Josephson junction.…”

An image cascaded two‐port model for single‐particle quantum propagation in crystals

“…A very effective way for describing quantum dynamical systems in terms easily understandable by electronic engineers is that of representing them by equivalent circuits [1,2]. Although the mapping of a quantum system on a classical one turns out to be impossible if the single parts of the two systems have to be put in mutual correspondence, a global mapping is successful in several instances, as this paper will show through the detailed analysis of an example.…”