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Acta Physica Sinica

Quantum dissipation of the density matrix of mesoscopic RLC circuit

Fan Hong‐Yi, He Rui

Published Jan 1, 2014• 1 citation
Publisher

Abstract

For the first time, as far as we know, we use the approach of solving the amplitude-decaying master equation of density matrix to study the quantum dissipation of a mesoscopic RLC circuit, and thus find out the attenuation law of circuit energy. We then use the entangled state representation and the technique of integration within an ordered product of operators to explore this problem.

DOI
10.7498/aps.63.110301

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For the first time, as far as we know, we use the approach of solving the amplitude-decaying master equation of density matrix to study the quantum dissipation of a mesoscopic RLC circuit, and thus find out the attenuation law of circuit energy. We then use the entangled state representation and the technique of integration within an ordered product of operators to explore this problem.
Quantum information processing experimentally depends on optical-electronic devices. In this paper, we consider quantized mesoscopic RLC (resistance, inductance and capacitance) electric circuit in stable case as a quantum statistical ensemble, and calculate energy distribution (i.e. the energy stored in inductance and capacitance as well as the energy consumed on the resistance). For this aim, we employ the technique of integration within ordered product (IWOP) of operator to derive the thermo-vacuum state for this mesoscopic system, with which ensemble average energy calculation is replaced by evaluating expected value in pure state. This approach is concise and the result we deduced is physically appealling.
Taking into consideration the interactions between electrons and phonons, we have studied the temporal evolution of the average charge and current in a dissipative mesoscopic RLC circuit. Our results show that a mesoscopic RLC circuit can be treated as an interactive system between an electromagnetic harmonic oscillator and many lattice harmonic oscillators; this is called the bathing of the harmonic oscillators. The results also show that the quantum equation of motion of the linear mesoscopic RLC circuit is identical in form to its classical equation of motion, the only difference between them being their respective meanings. In order to thoroughly study the quantum properties of a dissipative mesoscopic circuit, we have to consider not only the electromagnetic energy of the circuit, but also the crystal lattice vibration energy and the interactive energy between electrons and phonons.
Taking into consideration the interactions between electrons and phonons,we have studied the temporal evolution of the average charge and current in a dissipative mesoscopic RLC circuit.Our results show that a mesoscopic RLC circuit can be treated as an interactive system between an electromagnetic harmonic oscillator and many lattice harmonic oscillators;this is called the bathing of the harmonic oscillators.The results also show that the quantum equation of motion of the linear mesoscopic RLC circuit is identical in form to its classical equation of motion,the only difference between them being their respective meanings.In order to thoroughly study the quantum properties of a dissipative mesoscopic circuit,we have to consider not only the electromagnetic energy of the circuit,but also the crystal lattice vibration energy and the interactive energy between electrons and phonons.