Mesoscopic LC Circuit Research Articles

Selection Rules of Energy Level Transition for Mesoscopic LC Circuits with Complex Couplings

Selection Rules of Energy Level Transition for Mesoscopic LC Circuits with Complex Couplings

London superconductor and time-varying mesoscopic LC circuits

In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechanically, and can be mapped into a standard damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the aid of the dynamical invariant method and Fock states, we solve the time-dependent Schr\"odinger equation associated with this Hamiltonian and calculate some important physical properties of these systems such as expectation values of the charge and magnetic flux, their variances and the respective uncertainty principle.

Quantization of Foster mesoscopic circuit and DC–pumped Josephson parametric amplifier from fractal measure arguments

A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrödinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the associated creation and annihilation operators were obtained and analyzed. The quantization of the DC-driven Josephson circuit and its parametric amplifier were studied in details. The main outcome of this study concerns the finite form of the energy expectation value at very high temperature in contrast to the results obtained in literature which is time-dependent. Further details were analyzed and discussed. • The mesoscopic circuit and its quantum structure were explored using the concept of fractal product measure. • The theory is characterized by position-dependent electronic circuit's components. • The quantization of the DC-driven Josephson circuit and its parametric amplifier were constructed. • At very high temperature, a finite value of the energy expectation value was obtained.

Quantum disentangling operator and squeezed vacuum state’s noise of a mesoscopic two-loop LC circuit with mutual inductance

Quantum disentanglement refers to the transformation of entangled quantum system into disentangled system via some physical processes. In this paper, we search for quantum disentangling operator for the mesoscopic two-loop [Formula: see text] circuit with mutual inductance [Formula: see text]. It is this mutual inductance that causes quantum entanglement. By virtue of the method of integration within ordered product (IWOP) of operators, we find the disentangling operator and deduce the energy level (characteristic frequency). The quantum noise expression of squeezed vacuum state is also derived based on which we see that the large number of quantum entanglement engendered by the mutual inductance is, the more quantum noise produces in the mesoscopic circuit.

Characteristic frequency of a three-loop mesoscopic LC circuit with two non-symmetric mutual inductances

We use the Invariant eigenoperator (IEO) method to derive characteristic frequency of two-loop and three-loop mesoscopic LC circuit with non-symmetric mutual inductances. By searching for invariant eigenoperators of the Hamiltonian of mesoscopic LC circuits, we can calculate their energy-levels very conveniently. This method is quite concise and effective and has many applications in quantum mechanics. Thus we can calculate energy-levels by searching for invariant eigenoperators.

Wave function, equivalent inductance and magnetic energy stored in the mesoscopic two-loop L–C circuit derived in entangled state representation

We analyse the mesoscopic two-loop LC circuit in which a capacitance C is sharing and mutual inductance M exists between two inductances L1, L2. Instead of using the usual Kirhoff's voltage law to examine the equivalent inductance, we solve the Schrödinger equation for this quantized two-loop LC circuit to find the wave function in entangled state representation (ESR). In so doing, we derive the equivalent inductance L1L2−M2L1+2M+L2, and the quantized energy level formula En=L1I1+MI1+I2+L2I222L1+2M+L2+n+12L1+2M+L2L1L2−M2C, (n = 0, 1, …) where the term L1I1+MI1+I2+L2I222L1+2M+L2, as comparing the common energy stored in an inductance LI22, is a newly found magnetic energy stored in the two-loop circuit while quantum radiation with the characteristic frequency L1+2M+L2L1L2−M2C taking place. We do this by virtue of the ESR method, since quantum entanglement arises from both the mutual inductance coupling and the capacitance in sharing, and using ESR is convenient.

Radiating frequency of three-loop mesoscopic LC circuit with mutual inductance obtained by IEO method**Project supported by the National Natural Science Foundation of China (Grant No. 11775208).

Instead of normally tackling electric circuits by virtue of the Kirchhoff’s theorem whose aim is to derive voltage, 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 (IEO) method to realize our aim.

Quantum effect of cooling down the environment temperature of mesoscopic LC circuit

ABSTRACTWe examine the quantum effect of cooling down the environment temperature of mesoscopic LC circuit, and find that the ground state of the circuit is no longer in the thermo vacuum state, but in a negative binomial state. We calculate energy of the circuit in this new state, which increases with the cooling of the environment.

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.

An investigation of algebraic quantum dynamics for mesoscopic coupled electric circuits with mutual inductance

Based on the electrical charge discreteness, the Hamiltonian operator for the mutual inductance coupled quantum mesoscopic LC circuits has been found. The persistent current on two driven coupled mesoscopic electric pure L circuits (two quantum loops) has been obtained by using algebraic quantum dynamic approach. The influence of the mutual inductance on energy spectrum and quantum fluctuations of the charge and current for two coupled quantum electric mesoscopic LC circuits have been investigated.

On the dynamics of a time-dependent mesoscopic LC circuit with a negative inductance

We discuss the problem of a mesoscopic LC circuit with a negative inductance ruled by a time-dependent Hermitian Hamiltonian. Classically, we find unusual expressions for the Faraday’s law and for the inductance of a solenoid. Quantum mechanically, we solve exactly the time-dependent Schrödinger equation through the Lewis and Riesenfeld invariant operator method and construct Gaussian wave packet solutions for this time-dependent LC circuit. We also evaluate the expectation values of the charge and the magnetic flux in these Gaussian states, their quantum fluctuations and the corresponding uncertainty product.

介观LC电路在辐射场作用下约化密度方程的推导

介观LC电路不可避免会处于辐射场中，把辐射场看成是由无穷多谐振子组成的，选择介观LC电路为研究对象。本文从介观LC电路与辐射场相互作用的哈密顿量出发，把辐射场看成库，通过对库求迹，推导了介观LC电路在辐射场作用下的密度方程。 Quantum LC circuit locates inevitably in radiation field; the thermal radiation field is a reservoir which is described by infinite harmonic oscillators, and quantum LC circuit is a system to be investigated. From the interaction between mesoscopic LC circuit and radiation field, the radiation is reservoir. We trace out the reservoir and deduce the equation of density.

Evolution of Quantum State in the Mesoscopic LC Circuit Driven by a Time Dependent Source

We obtained the exact solution of time evolution by applying the Wei-Norman method.The quasi-probability distribution function of phase space is used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is the two dimensional motional gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.

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.

Study on the zero-state quantum responses for inductance coupled mesoscopic LC circuits

The exact solution of time-evolution operator is obtained by applying the gauge transformation of algebra dynamics. Such an operator describes the time-evolution of the quantum state for two inductance coupled mesoscopic LC circuits. The zero-state responses of the charge and current to the input voltage signal are calculated. The results show that the system of inductance coupled mesoscopic LC circuits is linear and time-invariant. The zero-state responses of the charge and current are consistent with those of the corresponding macroscopic circuit.

Quantum fluctuation in excited states of mesoscopic LC circuits at finite temperature

We discuss quantum fluctuation in excited states (named thermo number states) of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.

Thermal effect and energy-level transition rule for a mesoscopic LC circuit with inductance–capacitance coupling

This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the ‘invariant eigen-operator’ method, it deduces the energy-level transition rule when the system is disturbed by an external electromagnetic field. At the same time, the quantum fluctuations for the system at finite temperature are examined by virtue of the generalized Hellmann–Feynman theorem.

Thermal Effect for the Mesoscopic LC Circuits Including Complicated Coupling by Virtue of GHFT

The Hamilton operator for the mesoscopic LC circuits including complicated coupling is given. Because the practical circuits are inevitably influenced by the external environment, the effect of temperature on the quantum effects for the mesoscopic circuit must be taken into account. Then we discuss the thermal effect of the system by simulating it with the biphotonic process and the contribution of each process to the energy ensemble average by virtue of the generalized Hellmann-Feynman Theorem (GHFT).

Modified Josephson Equation for Mesoscopic Parallel LC Circuit Including a Josephson Junction

By introducing the entangled state representation, the Cooper-pair number–phase quantization of the mesoscopic parallel LC circuit including a Josephson junction is realized. In the Heisenberg picture, the modified Josephson equation associated with the modification of the Faraday equation about the inductance is deduced from the motion equation.