Endothelin and the ischaemic heart

Soon after its identification as a powerful vasoconstrictor peptide, endothelin (ET-1) was implicated as a detrimental agent involved in determining the outcome of myocardial ischaemia and reperfusion. Early experimental studies demonstrated that ETA selective and mixed ETA/ETB receptor antagonists can reduce infarct size and prevent ischaemiainduced ventricular arrhythmias in models of ischaemia/reperfusion, implying that ET-1 acts through the ETA receptor to contribute to injury and arrhythmogenesis. However, as our understanding of the physiology of ET-1 has expanded, the role of ET-1 in the ischaemic heart appears ever more complex. Recent evidence suggests that ET-1 exerts actions on the heart that are not only detrimental (vasoconstriction, inhibition of NO production, activation of inflammatory cells), but which may also contribute to tissue repair, such as inhibition of cardiomyocyte apoptosis. In addition, ET-1-induced mast cell degranulation has been linked to a homeostatic mechanism that controls endogenous ET-1 levels, which may have important implications for the ischaemic heart. Furthermore the mechanism by which ET-1 promotes arrhythmogenesis remains controversial. Some studies imply a direct electrophysiological effect of ET-1, via ETA receptors, to increase monophasic action potential duration (MAPD) and induce early after-depolarisations (EADs), while other studies support the view that coronary constriction resulting in ischaemia is the basis for the generation of arrhythmias. Moreover, ET-1 can induce cardioprotection (precondition) against infarct size and ventricular arrhythmias, through as yet incompletely understood mechanisms. To enable us to identify the most appropriate means of targeting this system in a therapeutically meaningful way we need to continue to explore the physiology of ET-1, both in the normal and the ischaemic heart

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $\nu = 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.Comment: 14 pages , revtex , IUCM93-00

Collective edge modes in fractional quantum Hall systems

Over the past few years one of us (Murthy) in collaboration with R. Shankar has developed an extended Hamiltonian formalism capable of describing the ground state and low energy excitations in the fractional quantum Hall regime. The Hamiltonian, expressed in terms of Composite Fermion operators, incorporates all the nonperturbative features of the fractional Hall regime, so that conventional many-body approximations such as Hartree-Fock and time-dependent Hartree-Fock are applicable. We apply this formalism to develop a microscopic theory of the collective edge modes in fractional quantum Hall regime. We present the results for edge mode dispersions at principal filling factors $\nu=1/3,1/5$ and $\nu=2/5$ for systems with unreconstructed edges. The primary advantage of the method is that one works in the thermodynamic limit right from the beginning, thus avoiding the finite-size effects which ultimately limit exact diagonalization studies.Comment: 12 pages, 9 figures, See cond-mat/0303359 for related result

Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which electric current and mechanical oscillation are treated fully quantum mechanically on an equal footing. Quantum mechanically fluctuating Aharonov-Bohm phases obtained by the electrons cause nontrivial contribution to mechanical vibration and electrical conduction of the wire. We demonstrate our theory by calculating the admittance of the wire which are influenced by the multiple interplay between the mechanical and the electrical energy scales, magnetic field strength, and the electron-electron interaction

Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect

We develop a simple kinetic equation description of edge state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect (IQHE), inter-mode equilibration is a prerequisite for quantization of the Hall conductance. Two sources for such equilibration are considered: Edge impurity scattering and equilibration by the electrical contacts. Several specific models for electrical contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions, such as $\nu=2/3$, these models for the electrical contacts {\it do not} equilibrate the edge modes, resulting in a non-quantized Hall conductance, even in a four-terminal measurement. Inclusion of edge-impurity scattering, which {\it directly} transfers charge between channels, is shown to restore the four-terminal quantized conductance. For specific filling factors, notably $\nu =4/5$ and $\nu=4/3$, the equilibration length due to impurity scattering diverges in the zero temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.Comment: 14 pages REVTeX, 6 postscript figures (uuencoded and compressed

Voltage-biased quantum wire with impurities

The bosonization technique to describe correlated electrons in a one-dimensional quantum wire containing impurities is extended to include an applied voltage source. The external reservoirs are shown to lead to a boundary condition for the boson phase fields. We use the formalism to investigate the channel conductance, electroneutrality, and charging effects.Comment: 4 pages REVTeX, incl one figure, to appear in Phys.Rev.Let

Effect of short-range electron correlations in dynamic transport in a Luttinger liquid

The density operator in the Luttinger model consists of two components, one of which describes long-wave fluctuations and the other is related to the rapid oscillations of the charge-density-wave (CDW) type, caused by short-range electron correlations. It is commonly believed that the conductance is determined by the long-wave component. The CDW component is considered only when an impurity is present. We investigate the contribution of this component to the dynamic density response of a Luttinger liquid free from impurities. We show that the conventional form of the CDW density operator does not conserve the number of particles in the system. We propose the corrected CDW density operator devoid of this shortcoming and calculate the dissipative conductance in the case when the one-dimensional conductor is locally disturbed by a conducting probe. The contribution of the CDW component to conductance is found to dominate over that of the long-wave component in the low-frequency regime.Comment: 6 pages, 4 figures; updated to the published versio

The effect of inter-edge Coulomb interactions on the transport between quantum Hall edge states

In a recent experiment, Milliken {\em et al.} demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the $\nu=1/3$ quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions which become dominant at low temperatures. Using renormalization group methods, we calculate the cross-over behaviour from Luttinger liquid to the Coulomb interaction dominated regime. The cross-over behaviour thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.Comment: 4 pages, RevTex, 2 postscript figures, tex file and figures have been uuencode

Mechanically induced current and quantum evaporation from Luttinger liquids

We investigate transport through a tunnelling junction between an uncorrelated metallic lead and a Luttinger liquid when the latter is subjected to a time dependent perturbation. The tunnelling current as well as the electron energy distribution function are found to be strongly affected by the perturbation due to generation of harmonics in the density oscillations. Using a semiconducting lead instead of a metallic one results in electrons being injected into the lead even without applied voltage. Some applications to carbon nanotubes are discussed.Comment: 7 pages, 2 figures (eps files