Quantum Transport with Dissipation: Linear and Non-Linear Response

We present a quantum transport equation derived under the simplifying assumption that the inelastic scattering is caused by uncorrelated point scatterers, such as magnetic impurities. While this assumption is not always realistic, we believe that the model can be used to describe much of the essential physics of quantum transport in mesoscopic systems. This assumption allows us to write a quantum transport equation that involves only the diagonal elements of the density matrix which we use to define a distribution function f(r; E). The kernel of this integral equation is calculated from the Schrodinger equation and contains all quantum interference effects. We show that at equilibrium the distribution function relaxes to the Fermi-Dirac function with a constant chemical potential everywhere in the structure. Assuming local thermodynamic equilibrium we then derive a linearized transport equation which has the appearance of a continuous version of the multiprobe Landauer formula. An alternative derivation is provided for the linearized transport equation starting from the multiprobe Landauer formula. Numerical results are presented for the conductivity of a disordered resistor with distributed inelastic scattering. A clear transition is observed from weak to strong localization as the inelastic scattering time is increased. In the present work we restrict ourselves to steady state transport and neglect many-body effects

An Integral Equation for Dissipative Quantum Transport

We present an integral equation derived under the simplifying assumption that the inelastic scattering is caused by uncorrelated point scatterers, such as magnetic impurities or impurities with internal degrees of freedom. While this assumption is not always realistic, we believe that the model can be used to describe much of the essential physics of quantum transport in mesoscopic systems. This assumption allows us to write a transport equation that involves only the electron density and not the spatial correlations of the wave function. The kernel of this integral equation is calculated from the Schrodinger equation and contains all quantum interference effects. We show that at equilibrium the electron density relaxes to the expected equilibrium value with a constant chemical potential everywhere in the structure. Assuming local thermodynamic equilibrium we then derive a linear-response transport equation which resembles the Landauer-Buttiker formula extended to include a continuous distribution of probes. An alternative derivation is provided in the appendix for the kernel of the linear-response transport equation, starting from the Kubo formula for the conductivity. We discuss the conditions under which this transport equation reduces to the well-known drift-diffusion equations describing classical Brownian motion. In the present work we restrict ourselves to steady state transport and neglect many-body effects beyond the Hartree term

Physicochemical properties of concentrated Martian surface waters

Understanding the processes controlling chemical sedimentation is an important step in deciphering paleoclimatic conditions from the rock records preserved on both Earth and Mars. Clear evidence for subaqueous sedimentation at Meridiani Planum, widespread saline mineral deposits in the Valles Marineris region, and the possible role of saline waters in forming recent geomorphologic features all underscore the need to understand the physical properties of highly concentrated solutions on Mars in addition to, and as a function of, their distinct chemistry. Using thermodynamic models predicting saline mineral solubility, we generate likely brine compositions ranging from bicarbonate-dominated to sulfate-dominated and predict their saline mineralogy. For each brine composition, we then estimate a number of thermal, transport, and colligative properties using established models that have been developed for highly concentrated multicomponent electrolyte solutions. The available experimental data and theoretical models that allow estimation of these physicochemical properties encompass, for the most part, much of the anticipated variation in chemistry for likely Martian brines. These estimates allow significant progress in building a detailed analysis of physical sedimentation at the ancient Martian surface and allow more accurate predictions of thermal behavior and the diffusive transport of matter through chemically distinct solutions under comparatively nonstandard conditions

Linear Response for Confined Particles

The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small perturbations of this nonuniform state is calculated from a linear Markov kinetic theory whose generator for the dynamics is exact in the short time limit. The kinetic equation is solved in terms of an effective mean field single particle dynamics determined by the local density and dynamical screening by a dielectric function for the non-uniform system. The autocorrelation function for the total force on the charges is discussed.Comment: 4 pages, 1 figure. Results presented at the "International Conference on Strongly Coupled Coulomb Systems", Camerino, Italy, July 2008. Submitted for publication in the conference proceedings (special issue of Journal of Physics A

Physics and Modeling of Submicron Devices. Annual Report: August I, 1987 - July 31, 1988

The work described in this report is directed at understanding quantum transport phenomena in sub-micron heterostructure devices, at developing computational techniques for modeling such devices, and at applying these techniques to develop new device concepts. During the past year we have (l) applied a previously developed collisionless quantum device model (SEQUAL) and Monte Carlo model (DEMON) to the design and study of heterojunction bipolar transistors (Chapter 2); (2) developed a technique for the analysis of arbitrarily shaped quantum devices with elastic scattering (Chapter 3); and (3) developed an approach for incorporating inelastic dissipative processes in quantum transport theory (Chapter 4). As a by-product of the research, several heterostructure device models have been developed: 1- and 2-D equilibrium models, 1- and 2-D drift-diffusion models, a I-D Monte Carlo simulator and a 1-D collisionless quantum device model. These simulation programs are being applied to advanced device analysis at a number of laboratories and are available to SRC members on reques

Physics and Modeling of Submicron Devices

The work described in this report is directed at understanding transport physics in sub-micron heterostructure devices, at developing computational techniques for modeling such devices, and at applying these techniques to investigate new device concepts. The focus of the past year’s work has been on extending our collisionless, quantum device models to treat elastic scattering processes and at applying previously-developed models to the design and study of AlGaAs/GaAs heterojunction bipolar transistors. This report describes the past year’s progress in these two areas. As a by-product of the research, several heterostructure device models have been developed, 1- and 2-D equilibrium models, 1- and 2-D drift-diffusion models, a 1-D Monte Carlo simulator and a 1-D, collisionless quantum device model. These simulation programs are being applied to advanced device analysis at a number of laboratories and are available to SRC members on request

Stock assessment of the Queensland and New South Wales pearl perch (Glaucosoma scapulare) fishery

Pearl perch (Glaucosoma scapulare) are found commonly in sub-tropical offshore-waters along the east coast of Australia and are a valuable table fish popular with commercial and recreational fishers. The species is long-lived, up to 30 years of age, and reaches sexual maturity at between 25 and 35 cm total length. Pearl perch are predominantly line-caught and fishing is managed separately by New South Wales (NSW) and Queensland. Historical fishing data indicate that pearl perch harvests have been consistently higher from Queensland waters with 73% of the total catch landed in Queensland in 2013. Approximately 52% of the Queensland catch is taken by recreational fishers compared with 42% in NSW. In Queensland, the Department of Agriculture and Fisheries (DAF) recently classified the stock status of pearl perch as “transitional depleting” (DAF Stock Status 2015). The status raised concern in both Queensland and NSW as to whether current management arrangements are adequate to protect the sustainability of pearl perch fishery. This stock assessment incorporates data from both jurisdictions and assesses at the whole of stock level; establishes current stock status reference points including biomass and fishing pressure levels for pearl perch; and provides advice on whether additional management measures are required to reduce fishing pressure and rebuild fish stocks

Quantum transport and momentum conserving dephasing

We study numerically the influence of momentum-conserving dephasing on the transport in a disordered chain of scatterers. Loss of phase memory is caused by coupling the transport channels to dephasing reservoirs. In contrast to previously used models, the dephasing reservoirs are linked to the transport channels between the scatterers, and momentum conserving dephasing can be investigated. Our setup provides a model for nanosystems exhibiting conductance quantization at higher temperatures in spite of the presence of phononic interaction. We are able to confirm numerically some theoretical predictions.Comment: 7 pages, 4 figure