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Notes: Abstract As the magnetic flux is increased (decreased) relative to the mid-plateau value by a given number of flux quanta, the 2-dimensional electron liquid responds by forming the same number of vortices (antivortices). Assuming the vortices (antivortices) to be pinned, we show that with a transport current flowing by, the pinning centres exert a force on the electron liquid. Inclusion of this force in a force balance equation for the electron liquid explains the formation of plateaus within the FQHE. The possibility of generalizing the theory to the IQHE is discussed.

Notes: Abstract One of the most promising implications of the phenomenological Ginzburg—Landau (GL) theory of superconductivity is the possible existence of current-carrying metastable states with a negative effective self-inductance. Microscopically this phenomenon can be explained as a result of the depairing mechanism which, when the center-of-mass velocityv s of the Cooper pairs is sufficiently large, can be so strong that a further increase ofv s will lead to a decrease of the total current. Using a one-dimensional formulation of the GL theory we investigate the thermodynamic stability of these states for different external constraints and obtain the result that a negative self-inductance can only be stable if the length of the system in the direction of the current is smaller than a critical value comparable to the GL coherence length λ/κ. It is an experimental fact that states of negative self-inductance are realized in Josephson junctions and other types of superconducting weak links because the dc supercurrent can be a decreasing function of the phase variable φ. The thermodynamic stability theory can therefore explain why weak links have to be short, and it also provides us with a unifying point of view by treating the phase φ and the current as a pair of thermodynamically conjugate variables for arbitrary one-dimensional systems. An important point is the operational phase definition as a thermodynamic parameter that can be controlled by the experimentalist. This requirement is essential for the general validity of the ac Josephson equation and it implies that φ must depend on the magnetic self-inductance of the system. By applying the GL theory to weak links we can delimit the validity of the usual dc Josephson equationI ∝ sin φ and see that deviations from this functional form are most likely to be found in thin-film bridges of the Anderson-Dayem (AD) type. When the currentI is the controlled variable the conjugate phase variable φ will fluctuate and the magnitude of these fluctuations depends strongly on the functional formI(φ). The phase fluctuations for constantI lead to a reduction of the critical current which will be absent when φ is the controlled variable. The observed microwave enhancement of the critical current in AD bridges, the so-called Dayem effect, can be explained as a result of a switch from current control to phase control, and the fluctuation formulae explain why the effect is negligible in structures exhibiting the classical Josephson sine law for the current-phase relation.