Time-dependent External Source 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.

Linear and nonlinear response for radiative heat transfer in many-body systems

A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body systems. By using response theory, explicit formula for the temperature and phase shifts is derived and expressed in terms of the amplitude and phase of external power sources. Although the proposed method is highly efficient because it can skip the transient response, it is valid when external powers are weak. As an illustration of this theoretical framework, we have shown the dynamics of temperatures in one, two, and three degree of freedom systems driven by sine wave input powers. Finally, we highlighted some emergent phenomena arising from purely dynamical many-body effects, including amplification, attenuation, delaying or accelerating temperature responses. This work could find important applications in the domain of dynamical thermal management at the nanoscale.

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.

Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expecta- tion values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.

Superconductor-normal metal quantum phase transition in dissipative and non-equilibrium systems

In physical systems, coupling to the environment gives rise to dissipation and decoherence. For nanoscopic materials, this may be a determining factor of their physical behaviour. However, even for macroscopic many-body systems, if the strength of this coupling is sufficiently strong, their ground-state properties and phase diagram may be severely modified. Also dissipation is essential to allow a system in the presence of a time-dependent perturbation to attain a steady, time-independent state. In this case, the non-equilibrium phase diagram depends on the intensity of the perturbation and on the strength of the coupling of the system to the outside world. In this paper, we investigate the effects of both dissipation and time-dependent external sources in the phase diagram of a many-body system at zero and finite temperatures. For concreteness, we consider the specific case of a superconducting layer under the action of an electric field and coupled to a metallic substrate. The former arises from a time dependent vector potential minimally coupled to the electrons in the layer. We introduce a Keldysh approach that allows to obtain the time dependence of the superconducting order parameter in an adiabatic regime. We study the phase diagram of this system as a function of the electric field, the coupling to the metallic substrate and temperature.

Generalized versus Selected Descriptions of Quantum <I>LC</I>-Circuits

Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed.

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.

Particle production in field theories coupled to strong external sources, II: Generating functions

We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a pair of solutions of the classical equations of motion, with non-standard temporal boundary conditions.

Particle production in field theories coupled to strong external sources, I: Formalism and main results

We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the color glass condensate. We derive a formula, in terms of cut vacuum–vacuum Feynman graphs, for the probability of producing a given number of particles. This formula is valid to all orders in the coupling constant. The distribution of multiplicities is non-Poissonian, even in the classical approximation. We investigate an alternative method of calculating the mean multiplicity. At leading order, the average multiplicity can be expressed in terms of retarded solutions of classical equations of motion. We demonstrate that the average multiplicity at next-to-leading order can be formulated as an initial value problem by solving equations of motion for small fluctuation fields with retarded boundary conditions. The variance of the distribution can be calculated in a similar fashion. Our formalism therefore provides a framework to compute from first principles particle production in proton–nucleus and nucleus–nucleus collisions beyond leading order in the coupling constant and to all orders in the source density. We also provide a transparent interpretation (in conventional field theory language) of the well-known Abramovsky–Gribov–Kancheli (AGK) cancellations. Explicit connections are made between the framework for multi-particle production developed here and the framework of reggeon field theory.

Adiabatic electron pumping through a quantum dot with a discrete level

An adiabatic electron pumping through a quantum dot with a discrete energy level under a magnetic field is investigated theoretically. Adiabatic spin pumping takes place under two time-dependent external sources, the Zeeman energy and the difference in the tunneling coupling to the dot between the left and right leads. The behavior of the pumped spin as a function of the amplitude of the magnetic field is different whether the dot level is above the Fermi level in leads.

Thermal hysteresis loop, dynamical breakdown, and emission-current spike in quantum-well photodetectors

A nonadiabatic sequential-tunneling model is developed and applied to explore the common origin of the transient behavior of electrons in quantum-well photodetectors in the presence of different time-dependent external sources, including device temperature, electric field, and incident optical flux. For the time-dependent temperature, a counterclockwise hysteresis loop in the tunneling current as a function of the swept temperature is predicted and attributed to a blockade or an enhancement of the sequential tunneling of electrons between quantum wells by the space-charge-field effect when the device temperature is swept up and then down. When a time-dependent electric field is applied, a dynamical breakdown of the photodetectors is predicted, where the peak of total current linearly increases with the frequency of an ac electric field from its static value under a dc field. This is due to the presence of an additional dielectric current, which is proportional to the oscillation frequency of the ac electric field and whose peak value becomes larger than the value of the saturated tunneling-current peak in the high-frequency domain. Under the dynamical-breakdown condition, the quantum-well photodetectors behave just like a uniform dielectric medium. In the presence of a time-dependent optical flux, an emission-current spike is predicted as a result of the dominant enhancement of the escape probability of electrons from quantum wells over the loss of electron density when an applied dc electric field is small. The experimental observations of the transient behavior of electrons in quantum-well photodetectors are successfully reproduced by our numerical calculations.

A STOCHASTIC MODEL FOR EPIDEMICS BASED ON THE RENEWAL EQUATION

A stochastic continuous-infection model is developed that describes the evolution of an infectious disease introduced into an infinite population of susceptibles. The proposed model is the natural stochastic counterpart of the deterministic model for epidemics, based on the renewal equation. As in the deterministic model, the infectivity of an infected individual is a function of his age-of-infection, that is the time elapsed since his own infection. A time-dependent external source of infection is included. The model provides analytical expressions that describe the stochastic infective-age structure of the population at any moment of time. It is shown that the mean value of the number of infectives predicted by the stochastic model satisfies the renewal equation, which furnishes a formal solution of this equation. The model also yields simple expressions for the expected arrival times of infectives, that can be useful for the inverse problem. An explicit expression for the final size distribution is obtained. This leads to a precise quantitative threshold theorem that distinguishes between the possibilities of a minor outbreak or a major build-up of the epidemic.

Least squares and integral methods for the spherical harmonic analysis of theSq-field

Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.