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International Conference on Nanotechnology

Circuit models for coupled Fermi oscillators

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Published Jan 1, 2009• 1 citation
OpenAlex

Abstract

There are several reasons for circuit modeling of quantum systems: the first is to establish a bridge between quantum and classical worlds, inasmuch this is possible, the second is to provide a unified view of quantum systems interacting with a macroscopic environment on the point of view of observations done on the latter, the third is the possibility of using circuit simulators to describe the performance of complex quantum systems. We discuss here the construction of equivalent circuits for coupled Fermi oscillators.

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There are several reasons for circuit modeling of quantum systems: the first is to establish a bridge between quantum and classical worlds, inasmuch this is possible, the second is to provide a unified view of quantum systems interacting with a macroscopic environment on the point of view of observations done on the latter, the third is the possibility of using circuit simulators to describe the performance of complex quantum systems. We discuss here the construction of equivalent circuits for coupled Fermi oscillators.
We discuss the concept of a mesoscopic wavefunction, first in a general context, as the concept of wavefunction has evolved, and then in a more specific context of modeling. The paper concentrates on a simple, abstract one-dimensional situation. In this context, there are three problems to be considered. In the first problem, we consider the construction of a wavefunction as a problem of interpolation, with information content in a multipoint perspective at finitely many discrete points and complete uncertainty elsewhere. The wavefunction is conceived abstractly as our unified subjective picture of information content. Each point of information is essentially free and independent of all others. This is a wavefunction for a classical system at the mesoscopic threshold. In the second problem, we consider how, using the concept of scaling and renormalization, the classical system can be brought to represent a mesoscopic level of integrated information, with points still treated as free, but now with the need to consider each point as an extended region, with possible boundary overlaps. We then, in the section on the third problem, consider modeling this renormalized system as an Ising-like system of interacting spins. This is the final picture we develop for a mesoscopic wavefunction. This can be viewed from the perspective of the evolution of the concept of wavefunction at the microscopic level, and we briefly discuss the new point of view being developed here. Finally, we present a discussion concerning the bearing of this on Gibbs phenomenon.
Investigamos varios metodos de simulacion cuantica de modelos fermionicos, y damos cuenta de una implementacion de una de nuestras propuestas en un soporte de circuitos superconductores. Partiendo de la usual codificacion digital de la informacion en qubits, habitual en computacion cuantica universal, modificamos este esquema central para incorporar tecnicas hibridas, donde no consideramos los qubits como unicos portadores de informacion, sino tambien otros elementos de las plataformas cuanticas, cuyos grados de libertad son recursos en potencia para almacenaje y computo. Atentos al concepto de ?complejidad simulando complejidad?, proponemos enfoques de simulacion cuantica digital-analogica y protocolos clasico-cuanticos para asi incrementar las capacidades de simulacion de fermiones en los circuitos superconductores. Proponemos su aplicacion para simulacion de modelos fermionicos en materia condensada, gravedad cuantica, teoria cuantica de campos, y quimica cuantica. Estos simuladores cuanticos especializados para ciertos problemas que usan codificacion analogica de la informacion son buenos candidatos para lograr la simulacion de problemas complejos en dispositivos cuanticos alcanzables con la tecnologia actual.
Einstein, De Broglie and others hoped that the schism between classical and quantum physics might one day be overcome by a theory taking into account the essential nonlinearity of elementary physical processes. However, neither their attempts, nor subsequent ones were able to supply a unifying principle that could serve as a starting-point for a coherent understanding of both microphysical and macroscopic phenomena. In the late 1960s the phenomenon of amplitude quantization, or Macroscopic Quantum Effect (MQE), was discovered in a class of nonlinear oscillating systems in which two or more subsystems are coupled to each other by interactions having a specific phase-dependent character -- so-called argumental interactions. Experimental and theoretical studies of the MQE, carried out up to the present time, suggest the possibility of a new conceptual framework for physics, which would provide a bridge between classical and quantum physics, replacing the Newtonian notion of "force" by a new conception of physical interaction. The present paper presents a brief introduction to the MQE and some ideas about its possible significance in the search for new approaches to the understanding of quantum phenomena.
The development of nanostructures as components of macroscopic electrical circuits puts into evidence the necessity of providing integrated models of the entire system. The most natural approach is to represent such nanostructures by equivalent circuits to be imbedded in the model of the macroscopic structure. In the paper we discuss to which extent such a task can be accomplished and in particular how it fits the available circuit software for numerical simulations. We present as a meaningful example the circuit model for an atom, described as a two-state quantum system, coupled with a single mode cavity in a n-photon state; such a simple system describes a quantum oscillator realized by the interaction of the electromagnetic field with matter.