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

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.

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

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.

PATH INTEGRAL SOLUTIONS OF RLC MESOSCOPIC CIRCUIT WITH SOURCE

In this paper, mesoscopic RLC circuit with source is studied with Feynman's path integral method. Resistance and source in the circuits make the quantization process rather complicated. To solve the problem, fluctuation analysis method is proposed to calculate the path integral propagator. Furthermore, the wave function and quantum fluctuation of the system are obtained, and time evolution characters of the system are discussed. The methods used in the paper would be helpful to the application of mesoscopic quantum theory.

FLUCTUATIONS AT FINITE TEMPERATURE AND THERMODYNAMICS OF MESOSCOPIC RLC CIRCUIT CALCULATED BY USING GENERALIZED THERMAL VACUUM STATE

By using the partial trace method and the technique of integration within an ordered product of operators we obtain the explicit expression of the generalized thermal vacuum state (GTVS) for an RLC circuit instead of using the Takahashi–Umezawa approach. According to thermal field dynamics (TFD), namely, the expectation value of physical observables in this GTVS is equivalent to their ensemble average, based on GTVS we successfully derive the quantum fluctuations at nonzero temperature and the thermodynamical relations for the mesoscopic RLC circuit. Our results show that the higher the temperature is, the more quantum noise the RLC circuit exhibits.