Oscillatory Function Of Time Research Articles

Time-periodic interaction between a spin-pair: A quantum master equation approach

Quantum master equations describe the dynamics of open quantum systems. Such systems might be subjected to external drives and internal interactions such as direct dipolar couplings. Both the external drives and the internal interactions could be oscillatory functions of time. In particular, a spin pair undergoing magic angle sample spinning experiences such oscillatory interactions in time. In the present work, we analyze a spin pair with a time-periodic interaction by using our recently-proposed fluctuation-regulated quantum master equation [PRA, 97, 063837 (2018)] (FRQME). FRQME helps calculate the first as well as the second-order effects of all time-dependent interactions Hamiltonians. Using FRQME, we find the usual sideband pattern and also have shown the linewidths of the sidebands as a function of the coupling strength, the period of oscillation, and an environmental parameter. We show that at high spinning speed, the sidebands would have a Lorentzian shape. We predict that the dipolar contributions to the sidebands’ linewidths are smaller for a shorter correlation time of the environmental fluctuations.

Kinetic approach to the Schwinger effect during inflation

Using the kinetic approach, we study the impact of the charged particle dynamics due to the Schwinger effect on the electric field evolution during inflation. As a simple model of the electric field generation, we consider the kinetic coupling of the electromagnetic field to the inflaton via the term ${f}^{2}(\ensuremath{\phi}){F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ with the Ratra coupling function $f=\mathrm{exp}(\ensuremath{\beta}\ensuremath{\phi}/{M}_{p})$. The production of charged particles is taken into account in the Boltzmann kinetic equation through the Schwinger source term. Produced particles are thermalized due to collisions which we model by using the collision integral in the self-consistent relaxation time approximation. We found that the current of created particles exhibits a non-Markovian character and cannot be described by a simple Ohm's law relation $j\ensuremath{\propto}E$. On the contrary, the electric current as well as the electric field are oscillatory functions of time with decreasing amplitudes and a phase difference due to the ballistic motion of charged carriers. Our qualitative results are checked by using a hydrodynamic approach. Deriving a closed system of equations for the number, current, and energy densities of charged particles and determining its solution, we find a good agreement with the results obtained in the kinetic approach.

On the forced flow around a rigid flapping foil

The two dimensional incompressible viscous flow past a flapping rigid foil immersed in a uniform stream is studied using a lattice-Boltzmann model. When the foil’s center of mass is fixed in space, numerical results reproduce the transition from the von Kármán (vKm) to the inverted von Kármán wake [T. Schnipper, A. Andersen, and T. Bohr, “Vortex wakes of a flapping foil,” J. Fluid Mech. 633, 411 (2009) and A. Das, R. K. Shukla, and R. N. Govardhan, “Existence of a sharp transition in the peak propulsive efficiency of a low pitching foil,” J. Fluid Mech. 800, 307 (2016)]. Beyond the inverted vKm transition, the foil was released. The numerical results show that the hydrodynamic forces on the flapper are oscillatory functions of time with amplitudes and mean values that scale with the square of the Strouhal number, defined with either the flapping amplitude or the flapper length that decays an order of magnitude when the foil is freed to swim. Upstream swimming consisted of a uniform horizontal motion and a vertical heaving. The swimming speed showed a linear dependence on the Strouhal number, defined with the amplitude of oscillation of the foil tip. As a consequence, thrust generated by the free flapper is related to the square of the swimming speed for moderate Reynolds numbers.

The Stationary SQUID

In the customary mode of operation of a SQUID, the electromagnetic field in the SQUID is an oscillatory function of time. In this situation, electromagnetic radiation is emitted, and couples to the sample. This is a back-action that can alter the state that we intend to measure. A circuit that could perform as a stationary SQUID consists of a loop of superconducting material that encloses the magnetic flux, connected to a superconducting and to a normal electrode. This circuit does not contain Josephson junctions, or any other miniature feature. We study the evolution of the order parameter and of the electrochemical potential in this circuit; they converge to a stationary regime and the voltage between the electrodes depends on the enclosed flux. We obtain expressions for the power dissipation and for the heat transported by the electric current; the validity of these expressions does not rely on a particular evolution model for the order parameter. We evaluate the influence of fluctuations. For a SQUID perimeter of the order of 1$\mu$m and temperature $0.9T_c$, we obtain a flux resolution of the order of $10^{-5}\Phi_0/$Hz$^{1/2}$; the resolution is expected to improve as the temperature is lowered.

Non-extensive entropy and properties of polaron in RbCl delta quantum dot under an applied electric field and Coulombic impurity

Bound polaron in RbCl delta quantum dot under electric field and Coulombic impurity were considered. The ground and first excited state energy were derived by employing Pekar variational and unitary transformation methods. Applying Fermi golden rule, the expression of temperature and polaron lifetime were derived. The decoherence was studied trough the Tsallis entropy. Results shows that decreasing (or increasing) the lifetime increases (or decreases) the temperature and delta parameter (electric field strength and hydrogenic impurity). This suggests that to accelerate quantum transition in nanostructure, temperature and delta have to be enhanced. The improvement of electric field and coulomb parameter, increases the lifetime of the delta quantum dot qubit. Energy spectrum of polaron increases with increase in temperature, electric field strength, Coulomb parameter, delta parameter, and polaronic radius. The control of the delta quantum dot energies can be done via the electric field, coulomb impurity, and delta parameter. Results also show that the non-extensive entropy is an oscillatory function of time. With the enhancement of delta parameter, non-extensive parameter, Coulombic parameter, and electric field strength, the entropy has a sinusoidal increase behavior with time. With the study of decoherence through the Tsallis entropy, it may be advised that to have a quantum system with efficient transmission of information, the non-extensive and delta parameters need to be significant. The study of the probability density showed an increase from the boundary to the center of the dot where it has its maximum value and oscillates with period T0=ℏ/ΔEwith the tunneling of the delta parameter, electric field strength, and Coulombic parameter. The results may be very helpful in the transmission of information in nanostructures and control of decoherence

Time-dependent factorial cumulants in interacting nano-scale systems

We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving away from the real-axis, the high-order factorial cumulants of the transport become oscillatory functions of time. Here we demonstrate this phenomenon on a model of charge transport through coherently coupled quantum dots attached to voltage-biased electrodes. Without interactions, the factorial cumulants are monotonic functions of the observation time. In contrast, as interactions are introduced, the factorial cumulants oscillate strongly as functions of time. We comment on possible measurements of oscillating factorial cumulants and outline several avenues for further investigations.

Comparison between kinetic and fluid simulations of slab ion temperature gradient driven turbulence

A detailed comparison between kinetic and fluid simulations of collisionless slab ion temperature gradient driven turbulence is made. The nondissipative closure model (NCM) for linearly unstable modes, which is presented by Sugama, Watanabe, and Horton [Phys. Plasmas 8, 2617 (2001)], and the dissipative closure model by Hammett and Perkins (HP) [Phys. Rev. Lett. 64, 3019 (1990)] are used in separate fluid simulations. The validity of these closure models for quantitative prediction of the turbulent thermal transport is examined by comparing nonlinear results of the fluid simulations with those of the collisionless kinetic simulation of high accuracy. Simulation results show that, in the saturated turbulent state, the turbulent thermal diffusivity χ obtained from the HP model is significantly larger than the χ given by the NCM which is closer to χ measured in the kinetic simulation. Contrary to the dissipative form of the parallel heat flux closure relation assumed in the HP model, the NCM describes well the exact kinetic simulation, in which for some unstable wave numbers k, the imaginary part of the ratio of the parallel heat flux qk to the temperature fluctuation Tk is a oscillatory function of time and sometimes takes positive values. The positive values of Im(qk/Tk), imply the negative parallel heat diffusivity, correlate with the occasional inward heat flux occurring for the wave numbers k, and reduce the total χ.

Wafer temperature measurement in a rapid thermal processor with modulated lamp power

Pyrometry methods utilizing modulated lamp power (“ripple”) were used to improve wafer temperature measurement and control in rapid thermal processing (RTP) for silicon integrated circuit production. Data from a manufacturing line where ripple pyrometers have been tested show significantly reduced wafer to wafer and lot to lot variations in final test electrical measurements and increased yields of good chips per wafer. The pyrometers, an outgrowth of Accufiber’s ripple technique, are used to compensate for ordinary production variations in the emissivities of the backsides of wafers, which face the pyrometers. Power to the heating lamps is modulated with oscillatory functions of time at either the power line frequency or under software control. Fluctuating and quasi-steady components in detected radiation are analyzed to suppress background reflections from the lamps and to correct for effective wafer emissivity. Sheet resistances of annealed wafers with high dose shallow As implants were used to infer temperature measurement capability over a range in backside emissivity. Emissivities are varied when depositing or growing one or more layers of silicon dioxide, silicon nitride, or polycrystalline silicon on the backsides of the wafers.

Tuning of the emission spectrum of a C3laser

An investigation was made of tuning of the emission spectrum of a semiconductor C3 (cleaved-coupled-cavity) laser. The radiation power carried by a mode was found to be an oscillatory function of time and current in the modulating part of the laser: a change in the current by less than 1 mA resulted in a smooth variation of the mode power from its maximum value to the spontaneous noise level. The rate of change of the emission frequency with the current in the modulating part was different for different lasers and depended in a complex manner on the current.

Nonlinear wave packets in the Kelvin-Helmholtz instability

The instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development. By using the method of multiple scaling, a generalized formulation of the amplitude equation is obtained, applicable to both stable and marginally unstable regions of parameter space. Of principal concern is the neighbourhood of the critical point for instability, where weakly nonlinear solutions can be found for arbitrary initial conditions. Among the analytical results, it is shown that (1) the nonlinear effects can be stabilizing or destabilizing depending on the density ratio, (2) the existence of purely spatial instability depends upon the frame of reference, the density ratio, and whether the nonlinear effects are stabilizing, (3) exact nonlinear solutions of the amplitude equation exist representing modulations of permanent form travelling faster than the signal velocity of the linear equation (in particular, a solution is found that represents a solitary wave packet), and (4) the linear solution to the impulsive initial value problem has 'fronts’ which travel with the two (multiple) values of the group velocity (the packet as a whole moves with the mean of the two values). Numerical solutions of the amplitude equation (a nonlinear, unstable Klein-Gordon equation) are also presented for the case of nonlinear stabilization. These show that the development of a localized disturbance, in one or two dimensions, is highly dependent on the precise form of the initial conditions, even when the initial amplitude is very small. The exact solutions mentioned above play an important role in this development. The numerical experiments also show that the familiar uniform solution, an oscillatory function of time only, is unstable to spatial modulation if the amplitude of oscillation is large enough.

The planar itinerant oscillator model. A discussion of its use in reproducing experimental data from three separate sources

Autocorrelation functions calculated from the itinerant oscillator model are compared with experimental data from far infrared absorption measurements, depolarised Rayleigh scattering measurements and molecular dynamics computations. It is concluded that the model represents the reorientation motion of a molecule in the fluid (at short times) satisfactorily. The predicted angular velocity aef is not a pure exponential but rather an oscillatory function of time. This seems to be the case generally for small molecules.

Analyse der Gestaltänderung von Aluminiumpulverpartikeln während eines Naßmahlvorganges / Analysis of Shape Alterations of Aluminium Powder Particles during a Wet-Milling Process

Contrary to brittle material, the equilibrium grainsize for ductile powders is often approached as an oscillatory function of time. The following paper investigates this behaviour by means of a geometrical analysis of the powder particles, using wet-milled aluminium powder as an example. For the description of the milling kinetics we have used Hüttig's milling functions which are obtained from a sieve analysis, the measuring of the specific area of a powder monolayer, and the determination of the space-filling.

Theoretical considerations of the temperature distribution in a channel bounded by two co-axial circular pipes

Solutions for the temperature distribution in a circular pipe have been given by various authors, notably Gretz, Nusselt, Goldstein; all these are cited in (1), section 266. I have already considered in one paper the temperature distribution in a circular pipe when viscous incompressible fluid is flowing through the pipe and rate of heat addition is an oscillatory function of time. In this paper expressions for the temperature distributions are derived when viscous incompressible fluid is flowing through the channel, the dissipation due to friction is neglected and the rate of heat addition is an exponential function of time. From the engineering point of view this situation has some importance.

The Oscillatory Character of the Variations in the Weights of Dairy Heifers

Summary Data are presented showing that the daily weights of growing dairy heifers receiving a non-roughage diet consist of a general trend plus an oscillatory function of time which tends to become less pronounced as the heifers increase in age and size. The behavior of the weights of these heifers when older was very similar to the behavior of the weights of yearling beef heifers fed on a normal alfalfa hay diet which indicates that the different behaviors at different ages observed for these heifers was a matter of age and not of diet. At any age there was always a tendency for a deviation from trend in a daily weight to depend on the deviations for the adjacent days. This fact must be considered in calculating the accuracy of the results of feeding trials. If weights that are used as the basis of conclusions in feeding trials happen to fall at the right parts of the natural oscillations, then very misleading results may be obtained. From the data presented it appears that for short time trials several animals should be included if possible, the environmental conditions be kept uniform, and frequent weighings throughout the trial should be made. For long-time trials, regular comparable weighings as often as possible should be made throughout the entire course of the trial.