Dissipative Currents Research Articles

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Energy balances for gravity currents with a jump at the interface produced by lock release

The exchanges of energy for an inviscid Boussinesq gravity current which is released from a lock and then propagates over a horizontal boundary are considered. In this study the depth ratio of ambient to lock, H, is smaller than 2; it is well known that in this case the interface of the current displays a backward-moving jump during the initial stage of the flow. The effects of this discontinuity on the energy balances are investigated using the two-layer shallow-water formulation. This is an extension of the work of Ungarish (Acta Mech 201:63–81, 2008) which covered only the smooth-interface case H ≥ 2. The energies in the current and in the ambient are calculated from numerical solutions of the initial-value shallow-water problem. Corresponding analytical energy balances are presented and the contribution of the backward-moving jump is elucidated. Both the numerical and analytical results indicate that, in general, the increase of kinetic energy of the shallow-water system cannot fully recover the decay of potential energy during the propagation. This imbalance (per unit time) of energy in the present lock-release time-dependent problem is well approximated by the rate of “dissipation” predicted by Benjamin’s (J. Fluid Mech 31:209–248, 1968) classical analysis of the steady-state current. The backward-moving jump enhances the dissipation when H is close to 1; however, for H > 1.4 (approximately) the contribution of this discontinuity to dissipation is insignificant. The general trend is that all shallow-water currents produced by lock-release are dissipative, and the dissipation increases with H. Three Froude-number formulas for the front-speed condition were considered, and it is concluded that Benjamin’s classical function is the most consistent with the motion of the jump, and produces the least dissipative currents.

The Electrolytic Actuator-An Effect Dominated by Dissipative Currents

For a conductive, elastic matter in thermodynamic equilibrium the LORENTZ force, which includes the COULOMB force for charged systems, is the only macroscopic interaction between the electromagnetic field and the matter. If irreversible currents such as diffusion and ionic currents are observed, these currents and their coupling can dominate the behaviour. Then, to describe that system it is necessary to start with a macroscopic description, which remains valid outside of the equilibrium. A macroscopic description of these currents is used to deduce a very simple model for an electrolytic actuator.

Comparative study of macroscopic quantum tunneling inBi2Sr2CaCu2Oyintrinsic Josephson junctions with different device structures

We investigated macroscopic quantum tunneling (MQT) of ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{y}$ intrinsic Josephson junctions (IJJs) for two device structures. One is a small mesa, which is a few nanometers thick with only two or three IJJs, and the other is a stack of a few hundred IJJs in a narrow bridge structure. The experimental results regarding the switching-current distribution for the first switch from the zero-voltage state were in good agreement with the conventional theory for a single Josephson junction, indicating that the crossover temperature from thermal activation to the MQT regime for the former device structure was similar to that for the latter device structure. Together with the observation of multiphoton transitions between quantized energy levels in the MQT regime, these results strongly suggest that the observed MQT behavior is intrinsic to a single IJJ in high-${T}_{c}$ cuprates and is independent of the device structure. The switching-current distribution for the second switch from the first resistive state, which was carefully distinguished from the first switch, was also compared with respect to the two device structures. In spite of the differences between the heat transfer environments, the second switch exhibited a similar temperature-independent behavior for both devices up to a much higher temperature than the crossover temperature for the first switch. We argue that this cannot be explained in terms of self-heating caused by dissipative currents after the first switch. As possible candidates for this phenomenon, the MQT process for the second switch and the effective increase in the electronic temperature due to the quasiparticle injection are discussed.

Extrinsic anomalous Hall effect in charge and heat transport in pure iron,Fe0.997Si0.003, andFe0.97Co0.03

We have investigated thermal and electrical Hall conductivities for nominally pure and impurity-doped iron to examine the skew-scattering-induced anomalous Hall effect in the low-temperature clean-limit regime. In Fe, ${\text{Fe}}_{0.997}{\text{Si}}_{0.003}$, and ${\text{Fe}}_{0.97}{\text{Co}}_{0.03}$, we have observed the steep change in the electrical and thermal Hall conductivities below 100 K. The abrupt change in the Lorenz numbers for the anomalous Hall component $({L}_{xy}^{A})$ that includes even the sign change signaling the opposite flow of charge and heat currents is also observed around the crossover temperature of Hall conductivity. These observations indicate the emergence of the dissipative anomalous Hall current induced by the skew scattering below 100 K.

Comparison between the first- and the second-junction switchings in a small stack of Bi2Sr2CaCu2Oy intrinsic Josephson junctions

We measured the switching current distributions of the first- and the second-junction switchings in a small stack of Bi2Sr2CaCu2Oy intrinsic Josephson junctions. Switching distribution for the first switching from the zero-voltage state became independent of temperature below 0.8 K suggesting the crossover from thermal activation to macroscopic quantum tunneling. On the other hand, switching distribution for the second switching from the first resistive state showed the similar temperature-independent behavior up to much higher temperature than the crossover temperature for the first switching. We argue that it cannot be explained in terms of self-heating owing to the dissipative currents after the first switching.

Nonextensive/Dissipative Correspondence in Relativistic Hydrodynamics

We argue that there is profound correspondence (the nonextensive/dissipative correspondence - NexDC) between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics which leads to simple expression for dissipative entropy current.

Magnetic flux in mesoscopic rings: Quantum Smoluchowski regime

Magnetic flux in mesoscopic rings under the quantum Smoluchowski regime is investigated. Quantum corrections to the dissipative current are shown to form multistable steady states and can result in statistical enhancement of the magnetic flux. The relevance of quantum correction effects is supported v ia the entropic criterion. A possible application for a qutrit architecture of quantum information is proposed.

Plasmon mechanism of resistance magnetooscillations in a two-dimensional electron system in strong electric fields

A multielectron approach is developed to explain the resistance magnetooscillations in two-dimensional electron systems that have recently been detected under the action of microwave pumping [1] or a strong dc electric field [23]. A qualitative change in the screened impurity potential in a strong electric field is taken into account for the first time. When considered in the rest frame of the center of the cyclotron orbit, the impurity potential becomes nonstationary and, thus, should be screened dynamically. This fact substantially changes the picture of impurity scattering in a “pure” two-dimensional system: a dissipative current is induced by the excitation of two-dimensional plasmons rather than by one-electron transitions between the Landau levels. In the case of microwave pumping, every period of resistance oscillation in a reciprocal magnetic field is formed by the excitation of the corresponding magnetoplasmon branch, and the fine structure of oscillations is formed by the singularities of the magnetoplasmon density of states. In a “dirty” two-dimensional system, the role of electron-electron interaction weakens, collective excitations cease to exist, and the results transform into the well-known results obtained in terms of a one-electron approach.

A note on the propagation speed of a weakly dissipative gravity current

This paper presents an experimental study on the propagation speed of gravity currents at moderate values of a gravity Reynolds number. Two cases are considered: gravity currents propagating along a rigid boundary and intrusive gravity currents. For the first case, a semi-empirical formula for the front propagation speed derived from simple energy arguments is shown to capture well the effect of flow deceleration because of viscous dissipation. In the second case, the propagation speed is shown to agree with the one predicted for energy-conserving virtually inviscid flows (Shin, Dalziel & Linden, J. Fluid Mech. vol. 521, 2004, p. 1), which implies that the losses due to vorticity generation and mixing at the liquid–liquid interface play only a minor role in the total balance of energy.

The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations

The present investigation explores the unsteady dynamics of large density contrast non-Boussinesq lock-exchange flows by means of high-resolution two-dimensional simulations of the incompressible variable-density Navier–Stokes equations, employing a combination of spectral and compact finite-difference methods. For small density contrasts, the simulations closely reproduce earlier Boussinesq results for corresponding flows. Across the entire range of density contrasts, good agreement is obtained between the computed front propagation velocities and corresponding experimental observations reported in Part 1 of this investigation and by other authors. The simulations yield the required quantitative information with respect to the light and dense front heights, their propagation velocities, and the spatial structure of the dissipation fields in order to determine conclusively which of the scenarios developed in Part 1 is observed in reality. Simulations are conducted for fluids with the same kinematic viscosity, as well as for fluids with the same dynamic viscosity. For both slip and no-slip boundary conditions, and for all values, we find that for larger density contrasts, the dense front dissipates an increasing amount of energy. In contrast, the energy dissipated by the light front remains near its Boussinesq level for all values of the density ratio. In addition, for all density ratios, the height of the light front is very close to half the channel height, and it propagates with a non-dimensional velocity close to a half. This provides strong evidence that the dynamics of the light front is indeed approximated by the energy-conserving solution described in an earlier theoretical analysis. In contrast, the height of the dense front is substantially less than half the channel height. In addition, its velocity is close to the value derived in Part 1 for a dissipative gravity current. Together with the above results for the dissipation field, this confirms that the dense front behaves as a dissipative gravity current.

Steady States of a Microwave-Irradiated Quantum-Hall Gas

We consider effects of a long-wavelength disorder potential on the zero conductance state (ZCS) of the microwave-irradiated 2D electron gas. Assuming a uniform Hall conductivity, we construct a Lyapunov functional and derive stability conditions on the domain structure of the photogenerated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find nonzero conductances, photovoltages, and circulating dissipative currents. In contrast, weak white-noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations.

Multiple Andreev reflections in weak links of superfluidHe3−B

We calculate the current-pressure characteristics of a ballistic pinhole aperture between two volumes of B-phase superfluid 3He. The most important mechanism contributing to dissipative currents in weak links of this type is the process of multiple Andreev reflections. At low biases this process is significantly affected by relaxation due to inelastic quasiparticle-quasiparticle collisions. In the numerical calculations, suppression of the superfluid order parameter at surfaces is taken into account self-consistently. When this effect is neglected, the theory may be developed analytically like in the case of s-wave superconductors. A comparison with experimental results is presented.

Textural Effects and Spin-Wave Radiation in Superfluid3He Weak Links

The Josephson coupling between two volumes of superfluid 3He-B also couples the phase difference to the spin-orbit texture of the order parameter. As a result, the equilibrium configuration of the macroscopic texture depends on the phase difference. If the junction is biased by a pressure head, the Josephson oscillations of the supercurrent are accompanied by an oscillation of the texture close to the junction. This leads to a radiation of spin waves from the weak link, and thus contributes to the dissipative dc currents flowing through it. PACS numbers: 67.57.De, 67.57.Fg, 67.57.Np.

Jump in c-axis transport at the Bragg glass–vortex glass transition

We present dynamical simulations of anisotropic three-dimensional superconductors with point disorder. We study the three-dimensional XY model with anisotropy and the external magnetic field along the c-axis. This model has been shown to have a first-order transition as a function of the intensity of point disorder. We add an external current drive to the model and include both supercurrents and dissipative currents in the dynamics. We obtain current–voltage curves as a function of disorder at finite temperatures with current applied along the c-axis. We will show how the nonlinear current–voltage curves change as a function of disorder intensity across the transition line. The first-order character of the transition shows up clearly as a jump in the nonlinear transport response along the c-axis.

Dissipative Currents in Superfluid3He-B Weak Links

Recent measurements of dissipative currents in pressure-biased weak links of superfluid 3 He-B are discussed. It is pointed out that the theoretical understanding of their results is unsatisfactory. As one candidate model to explain them, we consider the process of multiple Andreev reflections (MAR). Connection of MAR to bound quasiparticle states inside ballistic contacts is discussed. As an explicit example we analyze the current in a short pressurebiased ballistic 3 He-B constriction. It is shown that the dissipative part of the current does not depend on the spin-orbit rotation matrices.

Electric-Field Breakdown of Absolute Negative Conductivity and Supersonic Streams in Two-Dimensional Electron Systems with Zero Resistance/Conductance States

We calculate the current-voltage characteristic of a two-dimensional electron system (2DES) subjected to a magnetic field at strong electric fields. The interaction of electrons with piezoelectric acoustic phonons is considered as a major scattering mechanism governing the current-voltage characteristic. It is shown that at a sufficiently strong electric field corresponding to the Hall drift velocity exceeding the velocity of sound, the dissipative current exhibits an overshoot. The overshoot of the dissipative current can result in a breakdown of the absolute negative conductivity caused by microwave irradiation and, therefore, substantially effect the formation of the domain structures with the zero-resistance and zero-conductance states and supersonic electron streams.

Nonequilibrium Josephson effect in short-arm diffusive SNS interferometers

We study non-equilibrium Josephson effect and phase-dependent conductance in three-terminal diffusive interferometers with short arms. We consider strong proximity effect and investigate an interplay of dissipative and Josephson currents co-existing within the same proximity region. In junctions with transparent interfaces, the suppression of the Josephson current appears at rather large voltage, $eV\sim \Delta$, and the current vanishes at $eV\geq\Delta$. Josephson current inversion becomes possible in junctions with resistive interfaces, where the inversion occurs within a finite interval of the applied voltage. Due to the presence of considerably large and phase-dependent injection current, the critical current measured in a current biased junction does not coincide with the maximum Josephson current, and remains finite when the true Josephson current is suppressed. The voltage dependence of the conductance shows two pronounced peaks, at the bulk gap energy, and at the proximity gap energy; the phase oscillation of the conductance exhibits qualitatively different form at small voltage $eV<\Delta$, and at large voltage $eV>\Delta$.

Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the edges of the Hall bar, cannot be understood on the basis of existing equilibrium theories. To explain these experiments, we generalize the Thomas-Fermi--Poisson approach for the self-consistent calculation of electrostatic potential and electron density in {\em total} thermal equilibrium to a {\em local equilibrium} theory that allows to treat finite gradients of the electrochemical potential as driving forces of currents in the presence of dissipation. A conventional conductivity model with small values of the longitudinal conductivity for integer values of the (local) Landau-level filling factor shows that, in apparent agreement with experiment, the current density is localized near incompressible strips, whose location and width in turn depend on the applied current.

Physical processes in thin-film electroluminescent structures based on ZnS:Mn showing self-organized patterns

Physical processes in thin ZnS:Mn films and their relation to the formation of dynamical patterns in the electroluminescence of AC driven films are investigated. The technique of photo-depolarization-spectroscopy is used to investigate defect states in these films and it is shown that specific features in the spectra correlate with the observed self-organized patterns. Furthermore, the time dependence of the dissipative current is measured at the same samples and compared with current waveforms obtained from numerical simulations of a drift-diffusion model. The results are used to discuss the origin of the self-organized processes in ZnS:Mn-films.