Hydrodynamic Equations in Quantum Hall Systems at Large Currents

Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity appearing at the breakdown of the quantum Hall effect. The derivation is based on microscopic electronic processes consisting of drift motions in a slowly-fluctuating potential and scattering processes due to electron-electron and electron-phonon interactions. In contrast with the usual HDEQs, one of the derived HDEQs has a term with an energy flux perpendicular to the electric field due to the drift motions in the magnetic field. As an illustration, the current distribution is calculated using the derived HDEQs.Comment: 10 pages, 2 Postscript figures, to be published in J. Phys. Soc. Jpn. 71 (2002) No.

Hydrodynamic Equation for the Breakdown of the Quantum Hall Effect in a Uniform Current

The hydrodynamic equation for the spatial and temporal evolution of the electron temperature T_e in the breakdown of the quantum Hall effect at even-integer filling factors in a uniform current density j is derived from the Boltzmann-type equation, which takes into account electron-electron and electron-phonon scatterings. The derived equation has a drift term, which is proportional to j and to the first spatial derivative of T_e. Applied to the spatial evolution of T_e in a sample with an abrupt change of the width along the current direction, the equation gives a distinct dependence on the current direction as well as a critical relaxation, in agreement with the recent experiments.Comment: 4 pages, 1 Postscript figure, corrected equations, to be published in J. Phys. Soc. Jpn. 70 (2001) No.

Heating process in the pre-Breakdown regime of the Quantum Hall Efect : a size dependent effect

Our study presents experimental measurements of the contact and longitudinal voltage drops in Hall bars, as a function of the current amplitude. We are interested in the heating phenomenon which takes place before the breakdown of the quantum Hall effect, i.e. the pre-breakdown regime. Two types of samples has been investigated, at low temperature (4.2 and 1.5K) and high magnetic field (up to 13 T). The Hall bars have several different widths, and our observations clearly demonstrate that the size of the sample influences the heating phenomenon. By measuring the critical currents of both contact and longitudinal voltages, as a function of the filling factor (around $i=2$), we highlight the presence of a high electric field domain near the source contact, which is observable only in samples whose width is smaller than 400 microns.Comment: 4 pages, 5 igures, 7th International Symposium of Research in High Magnetic Fields, to be published in physica

Student perspectives on mental health support and services in the UK

Student mental health is an issue of growing concern. Past research indicates that many students are not accessing the support they require, which may in part be due to issues surrounding the standards of the available services. Using a participatory framework, the current study utilised a mixed-methods design to examine student experiences of National Health Service (NHS) mental health services and perspectives of peer support. An online survey was completed by 376 UK students to examine their experiences of NHS mental health services, as well as their attitudes towards peer support. Several improvements were identified for future NHS mental health services regarding reduced waiting times, better access to alternative treatments and facilitating more patient-centred communication. Benefits of peer support services were also noted, including the potential to normalise experiences and promote belonging. These findings have implications for understanding how we can best support students experiencing mental health difficulties

Electronic Processes at the Breakdown of the Quantum Hall Effect

Microscopic processes giving the energy gain and loss of a two-dimensional electron system in long-range potential fluctuations are studied theoretically at the breakdown of the quantum Hall effect in the case of even-integer filling factors. The Coulomb scattering within a broadened Landau level is proposed to give the gain, while the phonon scattering to give the loss. The energy balance equation shows that the electron temperature T_e and the diagonal conductivity sigma_{xx} exhibit a bistability above the lower critical electric field E_{c1}. Calculated values of E_{c1} as well as T_e and sigma_{xx} at E_{c1} are in agreement with the observed values in their orders of magnitude.Comment: 4 pages, 2 Postscript figures, submitted to the Journal of the Physical Society of Japa

Mesoscopic transport beyond linear response

We present an approach to steady-state mesoscopic transport based on the maximum entropy principle formulation of nonequilibrium statistical mechanics. Our approach is not limited to the linear response regime. We show that this approach yields the quantization observed in the integer quantum Hall effect at large currents, which until now has been unexplained. We also predict new behaviors of non-local resistances at large currents in the presence of dirty contacts.Comment: 14 pages plus one figure (with an insert) (post-script codes appended), RevTeX 3.0, UCF-CM-93-004 (Revised

Quantum Response at Finite Fields and Breakdown of Chern Numbers

We show that the response to an electric field, in models of the Integral Quantum Hall effect, is analytic in the field and has isolated essential singularity at zero field. We also study the breakdown of Chern numbers associated with the response of Floquet states. We argue, and give evidence, that the breakdown of Chern numbers in Floquet states is a discontinuous transition at zero field. This follows from an observation, of independent interest, that Chern numbers for finite dimensional Floquet operators are generically zero. These results rule out the possibility that the breakdown of the Hall conductance is a phase transition at finite fields for a large class of models.Comment: 16 pages, 8 eps figures, LaTeX2e with IOP style. Many changes, including new materia

The analytical value of the electron (g-2) at order alpha^3 in QED

We have evaluated in closed analytical form the contribution of the three-loop non-planar `triple-cross' diagrams contributing to the electron (g-2) in QED; its value, omitting the already known infrared divergent part, is a_e(3-cross) = 1/2 pi^2 Z(3) - 55/12 Z(5) - 16/135 pi^4 + 32/3 (a4 + 1/24 ln(2)^4) + 14/9 pi^2 ln(2)^2 - 1/3 Z(3) + 23/3 pi^2 ln(2) - 47/9 pi^2 - 113/48. This completes the analytical evaluation of the (g-2) at order alpha^3, giving a_e(3-loop) = (alpha/pi)^3 { 83/72 pi^2 Z(3) - 215/24 Z(5) + 100/3 [( a4 + 1/24 ln(2)^4 ) - 1/24 pi^2 ln(2)^2 ] - 239/2160 pi^4 + 139/18 Z(3) - 298/9 pi^2 ln(2) + 17101/810 pi^2 + 28259/5184 } = (alpha/pi)^3 (1.181241456...).Comment: plain TeX, 16 pages, 2 figures. Submitted to Physics Letters B. Two postscript files (z2.ps, zx1gen.ps) are include