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International Journal of Advanced Engineering Research and Science

Semiclassical Nonlinear Approach for Mesoscopic Circuit

H. Torres‐Silva, Diego Torres Cabezas

Published Jan 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.22161/ijaers/3.9.11

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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.
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.
The quantum theory for the dual LC mesoscopic coupled electric circuit with charge discreteness is briefly described. The quantum Kirchoff's moving equation, and energy spectrum of the mesoscopic coupled circuit is given under the non-interaction Hamilton digenstate vectors. The results show that, taking account of the charge discreteness, a evident change occurred for the equation of mesoscopic circuit, and the energy spectrum of the circuit are not only related with the circuit parameters, but depended the quantization character of the charge.
The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoscopic circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrödinger equation of the system is a four-order difference equation in representation. Using the extended perturbative method, the detail energy spectrum and wave functions are obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopic circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.
Based on the fact that a mesoscopic capacitor can be regarded as a mesoscopic tunnel junction, we quantized the mesoscopic LC circuit by using the rotating -wave approximation.The study shows: Considering the coupled energy of the meso scopic capacitor, the system of the mesoscopic LC circuit will be equivalent to a Kerr system. We also used the thermal field dynamic theory to investigate the thermal Kerr state at a definite temperature and calculated the quantum fluc tuation of both charge and magnetic flux, and discussed the results.