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IOSR Journal of Electrical and Electronics Engineering

Nonlinear Dynamics of a Quantum Mesoscopic Circuit

H. Torres- Silva, Diego Torres Cabezas

Published Apr 1, 2016• 0 citations
Publisher

Abstract

In this article we study the nonlinear dynamics of a quantum mesoscopic circuit in the range where the initial condition 0  ,that is, the initial normalized magnetic flux of the system which oscillate in the intervalThis circuit is modeled as a LC circuit with quantized electric charge excited by energy battery that can produce an electrical discreteness charge in LC quantum circuit in the form of narrow pulses.

DOI
10.9790/1676-1104045258

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In this article we study the nonlinear dynamics of a quantum mesoscopic circuit in the range where the initial condition 0  ,that is, the initial normalized magnetic flux of the system which oscillate in the intervalThis circuit is modeled as a LC circuit with quantized electric charge excited by energy battery that can produce an electrical discreteness charge in LC quantum circuit in the form of narrow pulses.
Based on energy conservation considerations we study the nonlinear dynamic behavior of a quantum mesoscopic circuit, which is characterized through parameters of inductance and capacitance.Nonlinearity is given by the initial conditions of magnetic flux and discreteness charge which oscillate in the interval [-0 α , + 0 α ], being 0 α the magnetic flux normalized by e 0/ q = φ h .This LC circuit with quantized electric charge is excited by energy battery that can produce an electrical discreteness charge on the capacitor.The dynamics of the mesoscopic circuit is highly nonlinear.Our results show for the magnetic flux a nearly square wave with an elongated period when compared with the linear case and a train of narrow pulses for the discrete charge.
A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.
The quantum theory for mesoscopic electric LC circuits with charge discreteness is briefly described. We take into account a resistance element (R) as an environment of the discrete-charge mesoscopic quantum LC circuit which is modeled by a Hamiltonian consisting of oscillators with continuous range of frequencies. Using a minimal coupling method, we investigate the quantum dynamics of this system. Hereby, the persistent current on a quantum damped L-design under the external potential source is obtained. Then, we write Heisenberg equations for a driven mesoscopic quantum RLC circuit with a dissipative term proportional to Ohmic damping and obtain persistent current on such a mesoscopic electric circuit.
We firstly demonstrate the main ideas of quantum theory for mesoscopic electric circuits, which we proposed several years ago. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a further development, we discuss the mesoscopic electric circuit in the presence of linear dissipation as well as magnetic flux. We propose a quantum Kirchoff equation for the LCR circuit and discuss the oscillations for different criterion factors. We also solve the energy spectra and eigenvalues of the physical current under a soluble symmetry hypothesis.