Acta Sinica Quantum Optica

Quantum Fluctuations of the Charge and Current in Mesoscopic Inductor Coupled Circuit with Alternating Source

Jianhua Huang

Published Jan 1, 2007• 0 citations

Abstract

In this paper, we study the quantum dynamics of a mesoscopic coupled circuit with alternating source with the help of Hermitian invariant theory. We obtain the accurate solution of the time dependent Schrdinger equation, calculate the quantum fluctuations of the charge and current in the circuit and get the expression of the nonadiobatic noncyclic geometric phase of the mesoscopic circuit.

Related papers

Linear invariants and the quantum dynamics of a nonstationary mesoscopic RLC circuit with a source

I. A. Pedrosa, J. Lemos de Melo, E. Nogueira

In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussian wave packet solutions for this electromagnetic oscillation circuit and employ them to calculate the quantum fluctuations of the charge and the magnetic flux as well as the associated uncertainty product. We also show that the width of the Gaussian packet and the fluctuations do not depend on the external power.

Modern Physics Letters BOct 20, 201411 citations

GEOMETRIC PHASE IN A MESOSCOPIC LC CIRCUIT WITH ALTERNATING SOURCE

Yinghua Ji, Juju Hu, Qing Liu +1 more

In this paper, we examine a mesoscopic LC circuit with alternating source and solve its time-dependent Schrödinger equation by selecting a proper Hermitian invariant operator. We study LR geometric phase in mesoscopic circuit system. Our results indicate that LR geometric phase is present at all times. In the evolution of the circuit system, it is a geometric phase factor accumulated by the wavefunction of external source's interaction with circuit system after nonadiabatic and noncyclic evolution. Its property lies in that it depends on the evolution path of the system wavefunction in the parameter space.

International Journal of Modern Physics BDec 27, 20060 citations

The Coulomb Blockade and Quantum Fluctuations of Mesoscopic Capacity Coupling Circuits

LI Ling-duan

Using the quantum theory for a mesoscopic circuit based on the discreteness of electric charges, the finite-differenced Schrodinger equation of the non-dissipative mesoscopic capacity coupling circuit are achieved. The quantum effect not only comes from the quanumnization of circuit but also that of charge. Only after the properties of charge quanumnization is considered can the Coulomb blockade effect of a mesoscopic circuit be discussed. The Schrodinger equation can be divided into two Mathieu equations in p-representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. And the fluctuations are the main noise sources of quantum in the mesoscopic circuit.

Journal of Tangshan Teachers CollegeJan 1, 20060 citations

Quantum Statistical Mechanics and Quantum Fluctuations with a Power Source in a Mesoscopic RLC Circuit

Fang Ming

According to the charge discrete values,mesoscopic RLC circuit with a power source has been quantized based on the full quantum theory of the mesoscopic circuit.Thus,a systemetic finite-difference Schrdinger equation has been obtained.In representation,the form of Schrodinger equation has been transformed into the standard Mathieu equation.In the WKBJ approximation,the energy level distribution of Mesoscopic RLC Circuit with a Power Source has been obtained,and then the average of and 2 in the ground state has been calculated.The problem of quantum fluctuations in Mesoscopic RLC circuit with a power source has been solved by quantum statistical mechanics.

Journal of Cangzhou Normal UniversityJan 1, 20120 citations

Quantum fluctuations of mesoscopic RLC circuit with sources and time-dependant resistances

B. Neouioua, Farid Benamira, M.A. Benbitour

We discuss the quantization of two mesoscopic coupled RLC circuits with sources and a time-dependent resistances. We use unitary transformations to decouple the system and calculate the charge-current fluctuations for each loop. An adequate time-dependent form of resistances is used to simplify the quantum evolution of the system. We find that the charge-current fluctuations verify the Heisenberg principle and decrease when the time elapses.

Modern Physics Letters BMay 25, 20150 citations

Analytical solution of driven time-dependent mesoscopic circuits

Jinying Ma, Yazhuo Yao, Ronghai Liu +3 more

When a time-dependent harmonic system is further driven by an external source, it presents significant challenges to obtaining analytical solutions for the system. This paper applies the Lewis-Riesenfeld invariant method to a mesoscopic time-dependent dissipative inductor-capacitor (RLC) circuit with an external source. By constructing quantum invariant Hermitian operators and introducing auxiliary equations that can describe the effects of external sources and resistance, we analytically solve the Schrödinger equation of the system. Taking an alternating current (AC) voltage source as an example, we derive the generalized coherent states of a mesoscopic time-dependent RLC circuit with an external source, calculate the quantum fluctuations of charge and current, and obtain their corresponding uncertainty relations. The results indicate that the time-dependent inductance and resistance disrupt the minimum uncertainty relation of the Glauble coherent states in driven time-dependent mesoscopic RLC circuits. This research contributes to the establishment of a quantum theory for mesoscopic circuits.

Scientific ReportsApr 2, 20260 citations