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Communications in Theoretical Physics

Density Matrix for Mesoscopic Distributed Parameter Circuits

Yinghua Ji, Wang Qi, Haimei Luo, Lei Min-Sheng

Published Mar 1, 2005• 1 citation
Publisher

Abstract

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix ρ( q , q ′,β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T . The higher the temperature is, the stronger quantum noise the circuit exhibits.

DOI
10.1088/0253-6102/43/3/034

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Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix ρ( q , q ′,β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T . The higher the temperature is, the stronger quantum noise the circuit exhibits.
Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for nondissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix p(q, q',β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.
Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for a non-dissipative distributed parameter circuit (a uniform transmission line). Quantum fluctuations of charge and current in the vacuum state are investigated by adopting the canonical transformation and unitary transformation method. Our results indicate that in distributed parameter circuits, quantum fluctuations, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.
In this paper we consider a non-dissipative distributed parameter circuit at a finite temperature T. We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation. Thermal field dynamic is used in our discussion. It is shown that distributing parameter circuits and quantum fluctuations, which also have distributing properties, are related to both the circuit parameters and the positions and the model of signals and temperature T. The higher the temperature, the more quantum noise the circuit exhibits. The research will be helpful to miniaturize intergreate circuits and electric components. It will be also significant for the futher study of the qualitities of mesoscopic system.
The quantization of a mesoscopic transmission line in accordance with the discreteness of electric charges is proposed under the Born–Von-Karmann periodic boundary condition. The finite-difference Schrödinger equation of the circuit has been obtained in charge representation, and the Schrödinger equation is transformed into Mathieu equation in current representation. The wavefunction and energy spectrum can be solved by adopting the canonical transformation and unitary transformation method. Our results indicate that in the transmission line, quantum fluctuation of currents, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.
Using the Lagrangian function,the Hamiltonian of the inductance coupling mesoscopic circuits is given.The Hamiltonian operator is diagonalized by introducing a unitary operator.By virtue of the generalized Hellmann-Feynman theorem,the quantum fluctuations of charge and its conjugate quantity for the system at finite temperature are investigated.It is found that,the quantum fluctuations of charge and its conjugate quantity have something to do with not only the parameters of the citcuit cells,but also the temperature.