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Chinese Journal of Physics

Minimal Coupling Approach to Quantum RLC Circuits

Hassan Pahlavani, Fardin Kheirandish

Published Apr 1, 2010• 5 citations
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Abstract

We consider a resistance element (R) as an environment of an LC circuit, which is treated as the main system modeled by a Hamiltonian containing an oscillator with a continuous range of frequencies. Using a minimal coupling method which is appropriate for dissipative quantum systems, we investigate the quantum dynamics of this system. The Heisenberg equation for such a dissipative system contains a dissipative term proportional to Ohmic damping. Some transition probabilities indicating the way energy flows between the subsystems are obtained.

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We consider a resistance element (R) as an environment of an LC circuit, which is treated as the main system modeled by a Hamiltonian containing an oscillator with a continuous range of frequencies. Using a minimal coupling method which is appropriate for dissipative quantum systems, we investigate the quantum dynamics of this system. The Heisenberg equation for such a dissipative system contains a dissipative term proportional to Ohmic damping. Some transition probabilities indicating the way energy flows between the subsystems are obtained.
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.
Quantum mechanics of a general one dimensional dissipative system investigated by it's coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a dissipative term proportional to velocity obtained. As an example, quantum dynamics of a damped harmonic oscillator as the prototype of some important one dimensional dissipative models investigated consistently. Some transition probabilities indicating the way energy flows between the subsystems obtained.