Magnetic-field dependence of low-temperature mobility in quasi-one-dimensional electron systems

We study the mobility of a quasi-one-dimensional (Q1D) electron system in the presence of an axial magnetic field at low temperatures. We consider the mobility limits for remote-impurity scattering, homogeneous-background scattering, interface-roughness scattering, and alloy-disorder scattering mechanisms. For a system in which all carriers are in the lowest subband, the electron-impurity interaction is modelled for the above cases, and analytic expressions are derived. Calculations appropriate for a GaAs Q1D structure are presented for typical wire radius R, electron density N, impurity density Ni, and applied magnetic field B

Effect of cross-sectional geometry on the RPA plasmons of quantum wires

The effect of cross-sectional geometry on both the intrasubband plasmon and intersubband plasmon of a quantum wire is investigated within a two-subband RPA scheme. Exact analytical electronic wavefunctions for circular, elliptical and rectangular wires are employed within the infinite barrier approximation. It is found that for fixed cross-sectional area and linear electron concentration, the intrasubband plasmon energy is only marginally dependent on the wire geometry whereas the intersubband plasmon energy may change considerably due to its dependence on the electronic subband energy difference. © 1994

Screening effects on the confined and interface polarons in cylindrical quantum wires

We study the contribution of confined and interface phonons to the polaron energy in quantum-well wires. We use a dispersionless, macroscopic continuum model to describe the phonon confinement in quantum wires of circular cross section. Surface phonon modes of a free-standing wire and interface phonon modes of a wire embedded in a dielectric material are also considered. Polaron energy is calculated by variationally incorporating the dynamic screening effects. We find that the confined and interface phonon contribution to the polaron energy is comparable to that of bulk phonons in the density range N=105-107 cm-1. Screening effects within the random-phase approximation significantly reduce the electron-confined phonon interaction, whereas the exchange-correlation contribution tends to oppose this trend at lower densities

Theory of plasmon-polaritions in superlattices

SIGLEAvailable from British Library Document Supply Centre- DSC:D83266 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Collective excitations in quasi-one-dimensional electron systems under a magnetic field

A study of the magnetoplasmons of a cylindrical quasi-one-dimensional electron system is given in the presence of an axial magnetic field B. A two-subband system is considered and the dispersion relations for both intrasubband and intersubband magnetoplasmons are obtained using the exact infinite wall eigenfunctions. It is demonstrated that the application of a longitudinal B changes the mode frequencies for both types of excitations. The model includes both local-field corrections, which are shown to be important, and the Hartree potential, which is given in closed form. © 1993 The American Physical Society

Optimal excitation of two dimensional Holmboe instabilities

Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However, these instabilities occur in limited bands in the parameter space. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that is obtained for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges as a persistent quasi-mode for parameter values for which the flow is stable. © 2011 American Institute of Physics

S3T stability of the homogeneous state of barotropic beta-plane turbulence

Zonal jets and nonzonal large-scale flows are often present in forced-dissipative barotropic turbulence on a beta plane. The dynamics underlying the formation of both zonal and nonzonal coherent structures is investigated in this work within the statistical framework of stochastic structural stability theory (S3T). Previous S3T studies have shown that the homogeneous turbulent state undergoes a bifurcation at a critical parameter and becomes inhomogeneous with the emergence of zonal and/or large-scale nonzonal flows and that these statistical predictions of S3T are reflected in direct numerical simulations. In this paper, the dynamics underlying the S3T statistical instability of the homogeneous state as a function of parameters is studied. It is shown that, for weak planetary vorticity gradient ß, both zonal jets and nonzonal large-scale structures form from upgradient momentum fluxes due to shearing of the eddies by the emerging infinitesimal flow. For large ß, the dynamics of the S3T instability differs for zonal and nonzonal flows but in both the destabilizing vorticity fluxes decrease with increasing ß. Shearing of the eddies by the mean flow continues to be the mechanism for the emergence of zonal jets while nonzonal large-scale flows emerge from resonant and near-resonant triad interactions between the large-scale flow and the stochastically forced eddies. The relation between the formation of large-scale structure through modulational instability and the S3T instability of the homogeneous state is also investigated and it is shown that the modulational instability results are subsumed by the S3T results. © 2015 American Meteorological Society

Statistical state dynamics of weak jets in barotropic beta-plane turbulence

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (zonostrophic instability), which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flowforming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide range of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the evolution of weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability. © 2019 American Meteorological Society

Emergence and equilibration of jets in beta-plane turbulence: Applications of stochastic structural stability theory

Stochastic structural stability theory (S3T) provides analytical methods for understanding the emergence and equilibration of jets from the turbulence in planetary atmospheres based on the dynamics of the statistical mean state of the turbulence closed at second order. Predictions for formation and equilibration of turbulent jets made using S3Tare critically comparedwith results of simulationsmade using the associated quasi-linear and nonlinear models. S3T predicts the observed bifurcation behavior associatedwith the emergence of jets, their equilibration, and their breakdown as a function of parameters. Quantitative differences in bifurcation parameter values between predictions of S3T and results of nonlinear simulations are traced to modification of the eddy spectrum which results from two processes: nonlinear eddy-eddy interactions and formation of discrete nonzonal structures. Remarkably, these nonzonal structures, which substantially modify the turbulence spectrum, are found to arise from S3T instability. Formation as linear instabilities and equilibration at finite amplitude of multiple equilibria for identical parameter values in the formof jetswith distinctmeridional wavenumbers is verified, as is the existence at equilibrium of finite-amplitude nonzonal structures in the form of nonlinearly modified Rossby waves. When zonal jets and nonlinearly modified Rossby waves coexist at finite amplitude, the jet structure is generally found to dominate even if it is linearly less unstable. The physical reality of the manifold of S3T jets and nonzonal structures is underscored by the existence in nonlinear simulations of jet structure at subcritical S3T parameter values that are identified with stable S3T jet modes excited by turbulent fluctuations. © 2014 American Meteorological Society

Cause-and-effect of linear mechanisms sustaining wall turbulence

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators and parametric instabilities from temporal mean flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified physical models. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean flow to the fluctuating velocities . To that end, we use cause-and-effect analysis based on interventions: manipulation of the causing variable leads to changes in the effect. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from to is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time arranged so that only transient growth is active, can faithfully represent the energy transfer from to as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from to in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence. © The Author(s), 2021. Published by Cambridge University Press