Damped Regime Research Articles

The effective dissipation in Nb/AlOx/Nb Josephson tunnel junctions by return current measurements

Measurements of temperature dependence of the return current in high quality Nb/AlOx/Nb Josephson junctions are presented. From the experimental data, we obtain the effective resistance, i.e., the effective dissipation, for the retrapping process, according to the generalized resistively shunted junction model proposed by Chen, Fisher, and Leggett. We present a careful analysis, based on a comparison between the measured temperature dependencies of both the return and the quasiparticle tunneling current. We find that the junction subgap conductance, which includes the quasiparticle and the quasiparticle-pair interference terms, is responsible for the return process. The measurements have been performed on various samples, in a wide range of critical current densities from 50 to 2250 A/cm2, covering different damping regimes and spanning over the high and low temperature limits. Junctions with low critical current density show ideal dissipation which makes the return current scale with temperature according to the BCS exponential behavior without flattening out effects. This result may be relevant for the possible use of Nb/AlOx/Nb junctions in macroscopic quantum coherence experiments, which strongly require a very low dissipation.

Revised Landau damping rates of magnetohydrodynamic waves in hot magnetized equilibrium plasmas and its consequences for cosmic ray transport in the interplanetary medium

A relativistic theory of transverse oscillations in hot, magnetized, isotropic equilibrium plasmas is presented. The special theory of relativity enters the description with the requirement that the particle masses depend on the particle velocities which themselves are limited by the speed of light. Using the relativistic Maxwell‐Boltzmann‐Jüttner (MBJ) distribution correctly describing the equilibrium state of a plasma, we formulate the dispersion relations for subluminal as well as superluminal waves, using the Trubnikov representation. For Landau damping of transverse wave modes, the so‐called cyclotron damping, an analytical expression generalizing earlier results to a relativistically correct form is derived. The theory is applied to an electron‐proton plasma, the main constituents of the interplanetary medium. Special consideration is given to the regime of weak damping of low‐and high‐frequency waves in the interplanetary plasma. The resulting dispersion relations and damping rates are used to determine cosmic ray transport parameters in the interplanetary medium, in particular the mean free path of solar energetic particles and the related modulation parameter of galactic cosmic rays in a simple diffusion‐convection modulation model. It is shown that at particle rigidities below about 109 V/c the mean free path and the modulation parameter are significantly different for cosmic ray protons, negations, and positrons because of the different handedness of the particles in the ordered interplanetary magnetic field and the different Landau damping rates of right‐handed and left‐handed circularly polarized plasma waves.

Radiatively Damped Density Waves in Optically Thick Protostellar Disks

The redistribution of angular momentum and mass in circumstellar disks by spiral density waves is governed by processes that dissipate the waves. Dissipation is usually attributed to unspecified nonlinear processes or an ad hoc viscosity. In this paper, we examine dissipation by radiative losses associated with the cyclic compression and expansion of disk material by the density waves. We consider linear, discrete modes in optically thick disks and use a simplified treatment of the radiative losses in order to assess the parameter dependences and importance of radiative damping. Wave action conservation principles are generalized to describe the effect of dissipation (by any means) and the consequent coupling of wave and disk energy and momenta. A relation is derived (in the WKBJ limit) between radial mass transport of disk material and the azimuthally averaged dissipation rate. A wave amplitude equation is similarly derived, which describes the radial evolution of wave angular momentum, and therefore the radial deposition of angular momentum in the disk. Associated with the equation is a characteristic damping length, proportional to the cooling time from the base state temperature times the radial wave speed, and a factor that depends weakly on optical depth. The damping length is used to define, in terms of the disk base state temperature and surface density, regimes of strong and weak radiative damping. Waves in warm disks may be damped close to the resonances at which they are excited, while waves in cold disks can propagate to distances at which other dissipative mechanisms may dominate. It is found that the boundary between these regimes cuts across values that are thought to have characterized the primitive solar nebula. Thus both strong and weak radiative damping may be encountered in circumstellar disks in general.

Electron transfer in the inverted region: Adiabatic suppression and relaxation hindrance of the reaction rate

Kramers’s model is applied to an electron transfer reaction in the inverted region. The reaction rate is considered at different values of the coupling matrix element and the damping, which is a measure of the interaction of the reaction coordinate with the other, nonreactive degrees of freedom of the system. The coupling characterizes overlap of the electron orbits of the donor and acceptor. It is shown that at the low/high damping the reaction rate is controlled by the slowest of the two rates. One is the thermally averaged transition rate (the reaction rate in the intermediate damping regime) and another one is the rate controlled by the energy/spatial diffusion. We demonstrate that the reaction rate as a function of the electron coupling shows a striking difference from the normal region case. The rate passes via maximum and decreases exponentially with the increase of the coupling.

Solvent–solute reaction path curvature effects on energy transfer corrections to the solute reaction rate

We present a new rate theory which accounts for anharmonicities (nonlinearities) in the solute potential (force) over the complete range of solvent damping. The theory is based on a new method for calculating energy diffusion rates which incorporates anharmonicity-induced solvent–solute reaction path curvature and is thus valid throughout the intermediate to large damping regimes. This energy diffusion factor is combined with the microcanonical variational transition state theory spatial diffusion correction factor. The new theory is applied to the case of a cubic solute potential coupled to a long time scale bath and shown to be significantly more reliable than the turnover theory of Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] in the Kramers turnover regime.

Curve crossing problem with dissipation: Uniform rate expression in diabatic representation

The approach based on identification of the quasi-ballistic collective mode using the variational transition state theory (VTST) is applied to evaluation of the radiationless transition rate in the diabatic representation. The results for the rate match smoothly with the corresponding results derived in the adiabatic representation. This implies that the uniform expression for the rate constitutes a good approximation to the exact result. Analytic expression for the renormalized barrier frequency for Ohmic dissipation in the high barrier limit is derived. The result for the adiabaticity parameter in the strong damping regime reduces to Zusman’s result. The effect of non-Ohmic dissipation on the electron transfer kinetics in polar solvents is explored. A new procedure for the determination of the quasi-ballistic mode, based on variation of the total flux, is suggested. The procedure reduces to the VTST procedure in the adiabatic limit. In the nonadiabatic limit the quasi-ballistic mode coincides with the original reaction coordinate independently of the dissipation strength.

A numerical test of activated rate theories for cusped and smooth potentials

A numerical study of the effect of dissipation on the radiationless transition rate in the adiabatic and solvent-controlled limits is presented. For light particle reactions, the nonlinearity of the potential surface in the vicinity of the barrier top is important, and the potential may be approximated as a cusped double well potential, provided that the nonadiabatic coupling is small compared to the thermal energy. Three different theoretical approaches for calculation of the thermally activated rate are analyzed and compared with exact numerical results. We find that Variational Transition State Theory (VTST) with a planar dividing surface, as well as the approach of Calef and Wolynes (CW), provide a good description of the rate of symmetric reactions. A rate expression suggested by Dekker is found to be the least accurate. The CW approach is most accurate in the strong damping regime, while VTST is better in the weak damping regime. The accuracy of both methods improves as the potential is smoothed. VTST and the CW expression are also found to give a reasonable description of asymmetric reactions, provided that the asymmetry is not too large.

A versatile interface light-scattering spectrometer

A spectrometer for the detection of laser light scattered by thermally excited capillary waves at fluid interfaces is described. Its optical system makes possible precise observations at capillary mode wave numbers high enough to avoid significant effects of instrumental resolution and permits the beam to be incident upon the fluid interface through either of the two adjacent fluid phases. Its performance was tested on the following three model systems at 20 degrees C: the free surfaces of water and 2-butanol, representing the oscillatory and critically damped capillary wave regimes respectively, and the interface between mutually saturated phases of these two liquids, representing the non-oscillatory regime. Accessible wave numbers for which effects of instrumental resolution were insignificant ranged between approximately 1*105 and 5*105 m-1. Values obtained for surface and interfacial tensions and viscosity agreed well with those obtained using a high-accuracy Wilhelmy plate tensiometer and a capillary viscometer.

Damped plasma waves in photoexcited plasma in semiconductors.

We analyze the hydrodynamic modes associated with carriers in a photoinjected plasma in a direct-gap polar semiconductor. In this paper we concentrate our attention on the carrier material motion. Resorting to a mechanostatistical approach to irreversible thermodynamics, the coupled equations of evolution for the charge density of electrons and holes are derived. They have the form of hyperbolic equations which imply collective damped wave propagation. The kinetic coefficients on which they depend are determined at this mechanostatistical microscopic level. The corresponding hydrodynamic modes are characterized: they consist of, besides the single quasiparticle (electrons and holes) excitations, two collective modes, namely, the acoustical and optical plasma waves. Their dispersion relations and lifetimes are obtained. These hydrodynamic modes are evidenced and further characterized through the calculation and analysis of the spectrum of Raman scattering of radiation by the carriers. The motion of the charge density is analyzed and we show how the damped wave regime goes over to the Fick-like diffusive regime in the limit of very large wavelengths and very low frequencies.

Activated surface diffusion: Are correlated hops the rule or the exception?

The migration of adsorbed atoms on crystal surfaces is considered. To describe the adatom motion one often uses a generalized Langevin equation (GLE). The time-dependent friction, which enters the GLE, is caused by the interaction with the crystal excitations. However, the explicit form of the time-dependent friction is not well known. We show that if the damping is associated with acoustic phonons and the coupling of the adatom with the surface is not too strong, then the friction is Ohmic. An explicit expression for the friction coefficient is given in terms of the basic physical parameters of the crystal and in terms of the activation energy of the adatom on the surface. We find that usually the diffusion occurs in the intermediate damping regime. In this regime nearest neighbor hops are most probable and transition state theory gives an excellent estimate for the rate of escape and for the diffusion coefficient. Using the recently developed turnover theory for surface diffusion [Phys. Rev. E 49, 5098 (1994)] we derive explicit expressions for the evolution of the time-dependent site distribution and compare it with an experiment where correlated hops have been observed. We conclude that even when the motion is one-dimensional, correlated hops are to be expected only for sufficiently high temperatures or for physisorbed atoms.

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays.

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.

Brownian dynamics simulation of rodlike polymers under shear flow

The highly nonlinear behaviors of rodlike polymers in nematic phase under shear flow are studied with Brownian dynamics simulation. The LebwohlLasher nematogen model is taken as the prototype of the simulation and the mean-field approximation is avoided. By considering the nearest-neighbor intermolecular interaction, the spatial orientational correlation is introduced and therefore the spatial inhomogeneity such as the multiple-domain effect can automatically be incorporated. The transient order parameters, birefringence axes, shear stresses and first normal stress differences are calculated. The important finding of this work is that the director wagging and damped oscillation share the same molecular origin as director tumbling. The only difference is that the system is split into micro-domains which tumble with different phase angles in the wagging and damped oscillation regimes. The tumbling of the director of the whole system is suppressed due to the spatial inhomogeneity of director fields and then the damped oscillation of macroscopic stresses becomes predominant. The negative first normal stress difference exists at moderate shear rates, where both elasticity and viscosity play important role. Our simulation results including some dimensionless scaling parameters find good agreement with experimental observations in literature.

Manifestations of spatially dependent friction in classical activated rate processes

Classical activated rate processes are examined for systems which are influenced by a spatially dependent friction on the reaction coordinate motion. In these systems, the spatial dependence of the friction kernel arises from nonlinear couplings between the reaction coordinate and a many-dimensional harmonic oscillator representation of the bath fluctuations. This model is thought to provide a reasonable representation of many charge transfer reactions in polar solvents. One of the systems studied corresponds to the case where the friction along the reaction coordinate is weaker in the region of the barrier than in the reactant and product states, while the second system exhibits the opposite behavior. In the first system, significant effects due to the nonlinear dissipation are found over the entire range of the friction strength. In the second system, the nonlinear effects are largely confined to the weak to intermediate damping regime, but they can be quite large. Interestingly, for some values of the nonlinearity parameters, the second system does not exhibit a simple single exponential rate behavior for a long period of time. Mathematical analysis is provided to help explain the computer simulation results in both the weak and strong damping limits of each system.

Crossover between the extremely low damping and moderate underdamped regime in the thermal activation theory: Preliminary experimental results

The problem of the decay of metastable state due to thermal activation is studied. Experimental data referring to the supercurrent decay of an underdamped Josephson junction are compared with Kramers theory and its recent improvements. Significative aspects of the crossover region between the extremely underdamped regime and the moderate underdamped one are discussed.

Incoherent tunneling at weak bias: Weak quantum damping

The quantum decay rate Γ = A exp(− B) of a metastable oscillator is studied for a quartic potential energy barrier model by means of a generalized version of Langer's “imaginary part of the free energy” method in the weak ohmic quantum damping regime. It is found (i) that the fully “dynamical” analytical continuation of the weak bias anomalous fluctuation mode of the “breathing bounce” configuration in the partition function for weak damping requires a generalization of the strong damping procedure presented in an earlier paper; (ii) that at sufficiently low temperature the dependence of Γ on the bias energy shows a characteristic transition from being thermal to quantal; and (iii) that upon accounting for the “inflection scattering” in the free exit space of an isolated single well system — i.e. at zero friction and at zero temperature — the result for Γ agrees with the escape rate found in another earlier paper from the pertinent Schrödinger equation by means of an extended WKB “outgoing waves” analysis. Inter alia the restrictions 12B exp(− h ̵ ω 0/2k B T) → 0 and 2πk B T/ h ̵ ω 0 → 0 arising from the “two-state” and “sudden-flip” approximations are removed, leading to e.g. typical T 2 - contributions in B similar to those occuring in the strong bias and strong damping regimes.

Effect of dissipation on thermal activation in an underdamped Josephson junction: First evidence of a transition between different damping regimes.

Les mesures de la duree de vie de l'etat de tension nulle dans une jonction Josephson unique avec hysteresis demontrent clairement l'existence de deux regimes d'amortissement. Les resultats sont obtenus dans un large intervalle de valeurs de l'amortissement a l'interieur de la region sous-amortie parce que la resistance d'amortissement depend exponentiellement de l'inverse de la temperature comme la resistance des quasi-particules de la jonction. L'etude penetre un peu plus avant dans le probleme epineux de la resistance d'amortissement dans le modele de la jonction shuntee par une resistance

Influence of excitation conditions on laser action in organic dye solutions

The relationship between the laser action in organic dye solutions with an output energy of ~ 102 J and the pump source characteristics is discussed. It is shown that the specified conditions are satisfied best by a cavity electric-discharge pump source operating under a near-critical damped oscillatory regime. The most effective method for attaining this regime is a reduction in the active resistance of an electric-discharge plasma by lowering the gas pressure in the discharge cavity, which also ensures an increase in the mechanical strength of the source. A comparison is made of the calculated and experimental energy parameters of a laser utilizing a solution of rhodamine 6G in ethyl alcohol with an output energy of 130 J.

A rheological model of polymers and glass-reinforced plastics

Network polymers and the corresponding glass-reinforced plastics are investigated for a homogeneous uniaxial state of stress and constant temperature. A physical law relating the high-elastic strain and the stress in explicit form with once-determined structural constants is obtained for the damped (bounded) creep regime. The theoretical solutions are compared with the experimental data for a glass-reinforced plastic based on unsaturated polyester resin and glass mat reinforcement.

Stability Diagrams for the Plasma Diode†

ABSTRACT The part played by collisional damping in tho performanoe of a planar plasma diode is considered theoretically. Whereas the absence of scattering processes in the cold plasma limit (dominated by transit time oscillations) led to a perfectly tractable solution in terms of a characteristic equation, the present analysis turns out to be quite complicated. The exact solution for the current—voltage response obtains in parametric form involving the transit time ; reduction to hyperbolic functions serves to emphasize the need for further piece-meal analysis. Such detailed elaborations are deferred for future treatment. Thus the present communication deals primarily with the deduction of stability diagrams allowing for energy-dependent scattering processes within the space charge. Three regimes of collisional damping are entertained. Moderato levels (intermediate case) are featured by passage through three operating regions as the voltage applied increases. For weak collisions, only two regions occur as...