Mesoscopic Electric Circuit Research Articles

The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

Josephson junction in the quantum mesoscopic electric circuits with charge discreteness

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

The persistent current and energy spectrum on a driven mesoscopic LC-circuit with Josephson junction

The quantum theory for a mesoscopic electric circuit including a Josephson junction with charge discreteness is studied. By considering coupling energy of the mesoscopic capacitor in Josephson junction device, a Hamiltonian describing the dynamics of a quantum mesoscopic electric LC-circuit with charge discreteness is introduced. We first calculate the persistent current on a quantum driven ring including Josephson junction. Then we obtain the persistent current and energy spectrum of a quantum mesoscopic electrical circuit which includes capacitor, inductor, time-dependent external source and Josephson junction.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger Liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the RG flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction, (iii) mesoscopic electric circuits.

Fluctuation relations for current components in mesoscopic electric circuits

We present a new class of fluctuation relations, to which we will refer as Fluctuation Relations for Current Components (FRCCs). FRCCs can be used to estimate system parameters when complete information about nonequilibrium many-body electron interactions is unavailable. We show that FRCCs are often robust in the sense that they do not depend on some basic types of electron interactions and some quantum coherence effects.

THE PERSISTENT CURRENT ON A DRIVEN MESOSCOPIC RLC CIRCUIT

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.

QUANTIZATION OF MESOSCOPIC QUARTZ PIEZOELECTRIC CRYSTAL EQUIVALENT CIRCUIT

In the framework of an advanced quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges, a mesoscopic quartz piezoelectric crystal equivalent circuit is quantized. To resolve the finite difference Schrödinger equation, an improved parameter perturbative method is proposed when WKB and perturbative method are inapplicable. With this method, the energy spectrum and wavefunctions of the system are obtained and used to calculate current quantum fluctuation as an application. The new method would be helpful to the application of the mesoscopic circuits quantum theory. Besides, the detail characters of energy spectrum and wavefunctions in the system would be helpful to the design of integrate circuit.

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.

DRIVEN MESOSCOPIC ELECTRIC CIRCUITS

The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated. The persistent current on a quantum ring using an algebraic approach have been obtained. The energy spectrum and the persistent current of a quantum LC-design mesoscopic circuit, with a time-dependent external source, have been found.

Macroscopic Quantum Coherent Phenomena in the Mesoscopic Electric Circuit

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrodinger equation of the mesoscopic electric circuit with external source which is the time function has been proposed. By using the instanton methods, the macroscopic quantum coherent phenomena and effective capacitance oscillation in the mesoscopic electric circuit have been addressed.

Effect of scattering in the mesoscopic pure L design electric circuit

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The effect of scattering in mesoscopic ‘pure’ inductance design circuit, just like in the mesoscopic metallic rings has been address. The quantum characteristics of charge diffusion has also been obtained explicitly. The case in finite temperature has been discussed as well.

Dynamic characteristics in the mesoscopic metallic rings

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The dynamic characteristics in mesoscopic metallic rings which is pure L design electric circuit in our theory have been discussed. The Wannier–Stark ladders, dynamic localization, Bloch oscillation and Landau–Zener tunnelling have been addressed.

Quantum effects of the mesoscopic LC electric circuit in thermal Kerr state

Based on the fact that a mesoscopic capacitor can be regarded as a mesoscopic tunnel junction, we quantized the mesoscopic LC circuit by using the rotating -wave approximation.The study shows: Considering the coupled energy of the meso scopic capacitor, the system of the mesoscopic LC circuit will be equivalent to a Kerr system. We also used the thermal field dynamic theory to investigate the thermal Kerr state at a definite temperature and calculated the quantum fluc tuation of both charge and magnetic flux, and discussed the results.

Dynamic theory for the mesoscopic electric circuit

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The minibands of quasienergy in LC design mesoscopic electric circuit have been found. In the mesoscopic “pure” inductance design circuit, just like in the mesoscopic metallic rings, the quantum dynamic characteristics have been obtained explicitly. In the “pure” capacity design circuit, the Coulomb blockade had also been addressed.

Dynamic Stark ladders in the mesoscopic metallic rings

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with external source which is the time function have been proposed. The mesoscopic metallic ring is regarded as a “pure” inductance design, and the dependence of the quasienergy spectrum on a parameter called the electric matching ratio is presented.

MESOSCOPIC CIRCUIT WITH LINEAR DISSIPATION

We firstly demonstrate the main ideas of quantum theory for mesoscopic electric circuits, which we proposed several years ago. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a further development, we discuss the mesoscopic electric circuit in the presence of linear dissipation as well as magnetic flux. We propose a quantum Kirchoff equation for the LCR circuit and discuss the oscillations for different criterion factors. We also solve the energy spectra and eigenvalues of the physical current under a soluble symmetry hypothesis.

Quantum theory of mesoscopic electric circuits in entangled state representation

We propose a concise quantization scheme for mesoscopic electric circuits which is in accord with the discreteness of electric charge. Our scheme is based on finding the correct explicit form of charge ascending and lowering operators. The charge eigenstate are derived from the appropriate entangled state representation. We show how the entangled state representation can play the role of constructing a concise and natural quantization scheme for mesoelectronics.

Dynamic localization in mesoscopic metallic rings

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The mesoscopic metallic ring is regarded as a “pure” inductance design, and the dynamic localization of current has been obtained explicitly.

Energy band suppression in mesoscopic metallic rings

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with an external source which is the time function is proposed. The mesoscopic metallic ring is regarded as a `pure' inductance design, and the energy band suppression in mesoscopic metallic ring is addressed exactly.

Josephson-Like Effects in the Mesoscopic Electric Circuit**The project supported by National Natural Science Foundation of China and Postdoctoral Science Foundation of China

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with external source which is a time function has been proposed. The Josephson-like effects in the mesoscopic electric circuit have been addressed.