Statistical theory of relaxation of high energy electrons in quantum Hall edge states

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio

Seeing (ultra)sound in real-time through the Acousto-PiezoLuminescent lens

In this contribution, we focus on a recently developed piezoluminescent phosphor BaSi2O2N2:Eu (BaSiON), and report on Acoustically induced PiezoLuminescence (APL). Insonification of the BaSiON phosphor with (ultra)sound waves leads to intense light emission patterns which are clearly visible by the bare eye. The emitted light intensity has been measured with a calibrated photometer revealing it is directly proportional to the applied acoustic power. As such, APL can be used to devise a simple but effective acoustic power sensor. Further, the emitted APL light pattern has a specific geometrical shape which we successfully linked to the pressure field of the incident (ultra)sonic wave. This is explicitly demonstrated for an ultrasonic (f = 3.3 MHz) transducer. By varying the insonification distance (from near- to far-field), multiple 2D slices of the transducer's radiation field light up on the BaSiON phosphor plate. By simply photographing these light patterns, and stacking them one after another, the 3D spatial radiation field of the ultrasonic transducer was reconstructed. Good agreement was found with both classical scanning hydrophone experiments and simulations. Recently we found that APL can also be activated by acoustic waves in the kHz range, thus covering a wide frequency range. Some first preliminary results are shown

Constrained Interactions and Social Coordination

We consider a co-evolutionary model of social coordination and network formation whereagents may decide on an action in a 2 x 2- coordination game and on whom to establish costly links to. We find that a payoff dominant convention is selected for a wider parameter range when agents may only support a limited number of links as compared to a scenario where agents are not constrained in their linking choice. The main reason behind this result is that constrained interactions create a tradeoff between the interactions an agent has and those he would rather have. Further, we discuss convex linking costs and provide suffcient conditions for the payoff dominant convention to be selected in mxm coordination games.

A quantum magnetic RC circuit

We propose a setup that is the spin analog of the charge-based quantum RC circuit. We define and compute the spin capacitance and the spin resistance of the circuit for both ferromagnetic (FM) and antiferromagnetic (AF) systems. We find that the antiferromagnetic setup has universal properties, but the ferromagnetic setup does not. We discuss how to use the proposed setup as a quantum source of spin excitations, and put forward a possible experimental realization using ultracold atoms in optical lattices

Pressure buildup during CO2 injection in brine aquifers using the Forchheimer equation

If geo-sequestration of CO2 is to be employed as a key emissions reduction method in the global effort to mitigate climate change, simple yet robust screening of the risks of disposal in brine aquifers will be needed. There has been significant development of simple analytical and semi-analytical techniques to support screening analysis and performance assessment for potential carbon sequestration sites. These techniques have generally been used to estimate the size of CO2 plumes for the purpose of leakage rate estimation. A common assumption has been that both the fluids and the geological formation are incompressible. Consequently, calculation of pressure distribution requires the specification of an arbitrary radius of influence. In this talk, a new similarity solution is derived using the method of matched asymptotic expansions. By allowing for slight compressibility in the fluids and formation, the solution improves on previous work by not requiring the specification of an arbitrary radius of influence. A large-time approximation of the solution is then extended to account for non-Darcy inertial effects using the Forchheimer equation. Both solutions are verified by comparison with finite difference solutions. The results show that inertial losses will often be comparable, and sometimes greater than, the viscous Darcy-like losses associated with the brine displacement, although this is strongly dependent on formation porosity and permeability

Improving the worthiness of the Elder problem as a benchmark for buoyancy driven convection models

An important trapping mechanism associated with the geosequestration of CO~2~ is that of dissolution into the formation water. Although supercritical CO~2~ is significantly less dense than water, experimental data reported in the literature show that the density of an aqueous solution of CO~2~ could be slightly greater. Under normal situations, the transfer of gas to solution is largely controlled by the relatively slow process of molecular diffusion. However, the presence of variable densities can trigger off gravity instabilities leading to much larger-scale convection processes. Such processes can potentially enhance rates of dissolution by an order of magnitude. Consequently there is a need for future performance assessment models to incorporate buoyancy driven convection (BDC). A major issue associated with BDC models is that of grid convergence when benchmarking to the Elder problem. The Elder problem originates from a heat convection experiment whereby a rectangular Hele-Shaw cell was heated over the central half of its base. A quarter of the way through the experiment, Elder (1967) observed six plumes, with four narrow plumes in the center and two larger plumes at the edges. As the experiment progressed, only four plumes remained. The issue is that depending on the grid resolution used when seeking to model this problem, modelers have found that different schemes yield steady states with either one, two or three plumes. The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem using a pseudospectral method