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Physica Scripta

Dynamics for a MesoscopicRLCCircuit with a Source

L. F. Wei, X. L. Lei

Published Jul 1, 2000• 12 citations
Publisher

Abstract

The dynamical problem of a mesoscopic RLC circuit with a source ruled by a time-dependent Hermitian Hamiltonian is exactly solved by algebraic method. The dynamical variations of the charge and current in a mesoscopic RLC circuit with a dc or ac source are studied in detail. In particluar, we have shown that squeezed coherent states of light field can be generated in a mesoscopic RLC circuit driven by an external source, although their quantum statistical properties are not dependent of the external source.

DOI
10.1238/physica.regular.062a00007

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The dynamical problem of a mesoscopic RLC circuit with a source ruled by a time-dependent Hermitian Hamiltonian is exactly solved by algebraic method. The dynamical variations of the charge and current in a mesoscopic RLC circuit with a dc or ac source are studied in detail. In particluar, we have shown that squeezed coherent states of light field can be generated in a mesoscopic RLC circuit driven by an external source, although their quantum statistical properties are not dependent of the external source.
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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.
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.