Quantum fluctuations of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling

Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.

The Squeezing Effect in a Mesoscopic RLC Circuit

Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.

Quantum Fluctuation of a Mesoscopic Inductance Coupling Circuit at Finite Temperature

We study the quantization of mesoscopic inductance coupling circuit and discuss its time evolution. Bymeans of the thermal field dynamics theory we study the quantum fluctuation of the system at finite temperature.

Number-phase quantization of a mesoscopic RLC circuit

With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of.the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.

Radiating frequency of three-loop mesoscopic LC circuit with mutual inductance obtained by IEO method

Instead of normally tackling electric circuits by virtue oI the Klrctllaott＇s theorem wnose aim is to uerlvc voxt^gc, electric current, and electric impedence, our aim in this paper is to derive the characteristic frequency of a three-loop mesoscopic LC circuit with three mutual inductances, e.g., for the radiating frequency of the three-loop LC oscillator, we adopt the invariant eigen-operator （lEO） method to realize our aim.

Quankum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state.Our results show that the system state will evolve to a squeezed coherent state under the effect of external source.We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation.When the circuit has no dissipation or there is complete coupling between two meshes,the squeezing amplitude parameter only depends on the capacitance's ratio.

Quantum Effects of Mesoscopic Inductance and Capacity Coupling Circuits

基于电的费用，非消散的 mesoscopicinductance 的有限差别的 Schroedinger 方程和能力联合电路的 discretenes 为一个 mesoscopic 电路使用量子论被完成。库仑封锁效果，被电的费用的组件引起，被学习。适当地在电路选择部件，有限差别的 Schroedinger 方程能在 prepresentation 被划分成二个 Mathieu 方程。与 WKBJ 方法，处于二个电路的扎根的状态的水流量变化是计算的。结果表演水流量二个电路的零点的变化是存在并且相关。

Evolution of Quantum State for Mesoscopic Circuits with Dissipation

Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially.

Study on Quantum Entanglement Between Mesoscopic Circuit and Environment at Coherent State

Taking into account the interaction between electrons and phonons,in the case without-rotating-waveapproximation,we study the entangling property between the mesoscopic circuit and environment at coherent state orequilibrimn state.The result indicates that,in long time limit t→∞,the averages of charge and current in the circuitonly depend on the average of the system at the initial state when the environment is initially at thermal equilibrium.However,when the environment is initially at coherent state,the average of charge and current in the circuit is determinedby the specific coherent state ensemble.Generally speaking,the entanglement between the circuit and environment willlead to the quantum state purity declining of the circuit,then the circuit emerges decoherent phenomenon,and so amixed state appears.Purity changes are related to the initial quantum state of environment and circuit.With thefurther evolution of time,coherence will be gradually restored,but cannot return to 1.

Investigating mesoscopic circuits with entangled state representations

By employing the continuous parameter entangled state representations, we investigate the energy level and the wave function for a capacitively and mutual-inductively coupled LC mesoscopic circuit. It is found that investigating the meso- scopic circuit in such representations can bring us the following conveniences. Firstly, the dynamical equation is naturally transformed into a single-variable differential equation. Second/y, the center-of-mass kinetic energy is included in the energy level of the system. Thus it is instructive to introduce the entangled state representation into the investigation of mesoscopic circuits.

Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit

The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator,due to diodesincluded in the circuit.In this paper,using the advanced quantum theory of mesoscopic circuits,which based on thefundamental fact that the electric charge takes discrete value,the diode included mesoscopic circuit is firstly studied.Schr(o|¨)dinger equation of the system is a four-order difference equation in (?) rep esentation.Using the extended perturbativemethod,the detail energy spectrum and wave functions are obtained and verified,as an application of the results,thecurrent quantum fluctuation in the ground state is calculated.Diode is a basis component in a circuit,its quantizationwould popularize the quantum theory of mesoscopic circuits.The methods to solve the high order difference equationare helpful to the application of mesoscopic quantum theory.

Invariants and Quantum Fluctuations of a Mesoscopic RLC Circuit in a Squeezed State and Squeezed Number State

为与力量来源一起的一个 mesoscopic RLC 电路的 invariants 被学习并且过去常构造挤压的状态并且为系统挤压了数字状态。处于挤压的状态和挤压的数字状态的 mesoscopic RLC 电路的量变化也被调查。

Pancharatnam Phase of a Mesoscopic Coupled Circuit

We derive a formula of the nonadiabatic noncyclic Pancharatnam phase for a mesoscopic circuit with coupled inductors and capacitors. It shows that, because of coupling effect, the circuit is in squeezed quantum state initially, and the time evolution of Pancharatnam phase exhibits an oscillation in a complex way. Especially we find that when the capacity of the coupled capacitors is larger than that of other ones in the circuit, with the variation of time Pancharatnam phase becomes nearly periodic square-wave, which perhaps can provide a new approach for the realization of quantum logic gate.

Density Matrix for Mesoscopic Distributed Parameter Circuits

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.

The Squeezing Effect in a Mesoscopic RLC Circuit

Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.

Quantum Effect in Mesoscopic Open Electron Resonator

The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior:conductance oscillations.In this paper,using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen,the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value.With presentation transformation and unitary transformation,the Schr(?)dinger equation becomes an standard Mathieu equation.Then,the detailed energy spectrum and wave functions in the system are obtained,which will be helpful to the observation of other characters of electron resonator.The average of currents and square of the current are calculated,the results show the existence of the current fluctuation,which causes the noise in the circuits,the influence of inductance to the noise is discussed.With the results achieved,the stability characters of mesoscopic electron resonator are studied firstly,these works would be benefit to the design and control of integrate circuit.

Number-Phase Quantization Scheme for L-C Circuit

For a mesoscopic L-C circuit,besides the Louisell's quantization scheme in which electric charge q andelectric current I are respectively quantized as the coordinate operator Q and momentum operator P,in this paperwe propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangianformalism.The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.

Nonzero Temperature Squeezing of the Time—Dependent Harmonic Oscillator and the Applications to the Capacitive Coupled Electric Circuit

A new way to calculate the nonzero temperature quantum fluctuations of the time-dependent harmonicoscillator is proposed and the properties of squeezing are exactly given. The method is applied to the capacitive coupledelectric circuit. It is explicitly shown that squeezing can appear and the squeezing parameters are related to the physicalquantities of the coupled circuit.

Squeezing effect in the coupled mesoscopic electric circuits

The rapid development of nanotechnology and nanoelectronics has made it possible to minimize the integrated circuits and components towards atomic-scale dimensions. Clearly, when the transport dimension reaches a characteristic dimension, namely the