State Rho Research Articles

Bistability in the current-induced breakdown of the quantum Hall effect

The structure of the longitudinal resistance in the breakdown behaviour of the quantum Hall effect (QHE) of GaAs/AlGaAs heterostructures is studied at a temperature of about 100 mK using samples with a constricted current path. Time-resolved measurements on a sample with a 50 mu m wide constriction show that the current-induced breakdown of the QHE evolves as a switching between at least two states, a non-dissipative one and a resistive one. The two states may coexist in some region of magnetic field and sample current. This shows up in the time behaviour of the longitudinal voltage, which is time-distributed in a statistical manner. Increasing the sample current at fixed magnetic field increases the time the current carriers stay in the resistive state rho dis until at high enough currents all backswitching into the non-dissipative state is suppressed. At filling factors nu <or=2, the resistivity rho dis increases linearly with the difference Delta nu = nu - nu i with nu i=2. The corresponding voltages are found to be less than h(cross) omega c/e at all sample currents, contrary to results of Cage et al. (1990). For filling factors with nu >or=2 the sample shows no similar effect. The results are discussed within the framework of several existing models for the breakdown behaviour of the QHE.

Kantowski-Sachs multidimensional cosmological models and dynamical dimensional reduction

Einstein's field equations are solved for a multidimensional spacetime (KS)*Tm, where (KS) is a four-dimensional Kantowski-Sachs' spacetime (1966) and Tm is an m-dimensional torus. Among all possible vacuum solutions there is a large class of spacetimes in which the macroscopic space expands and the microscopic space contracts to a finite volume. The authors also consider a non-vacuum case and they explicitly solve the field equations for the matter satisfying the Zel'dovich equations of state (1987). In non-vacuum models, with matter satisfying an equation of state rho = gamma rho . O<or= gamma rho (1, at a sufficiently late stage of evolution the microspace always expands and the dynamical dimensional reduction does not occur. Models (KS)*B(IX)*S1*S1*S1*S1 and (KS)*B(IX)*B(IX)*S1, where B(IX) is the Bianchi type-IX space, are also briefly discussed. It is shown that there is no chaotic behaviour in these cases. The same conclusion is also valid when one-loop high-temperature quantum corrections generated by a massless scalar field are taken into account.

A Boltzmann map for quantum oscillators

The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega/sub 1/, omega/sub 2/, and omega/sub 3/ mutually irrational, but obeying a relation n/sub 1/omega/sub 1/ + n/sub 2/omega/sub 2/ = n/sub 3/omega/sub 3/, n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) ..beta../sub 1/, ..beta../sub 2/, ..beta../sub 3/ obeying the equation n/sub 1/omega/sub 1/..beta../sub 1/ + n/sub 2/omega/sub 3/..beta../sub 1/number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case.

Electromagnetic mass models in general relativity: Lane-Emden-type models.

Imposing an equation of state rho+p-italic = 0, rho>0 (''false vacuum'') on a static spherically symmetric charged perfect-fluid distribution, various electromagnetic mass models are derived. It is shown that the modified field equations suggested by Einstein to study the equilibrium structure of an ''electron'' form a part of the field equations considered by us in this paper. Assuming an implicit relation among the unknown physical parameters, viz., the pressure p-italic, charge density sigma, and the electromagnetic potential Phi, it is shown that Phi satisfies the well-known Lane-Emden equation. Electromagnetic mass models corresponding to the exact solutions of the Lane-Emden equation are obtained. The radii of some of the models are compared with the ''classical electron radius.''

Characterisations of compatibility, comparability and orthogonality of quantum propositions in terms of chains of filters

Let p(F.E, rho ) denote the probability of a yes result of the yes-no effect obtained by putting the filter of the quantum proposition F (a projection operator) after that of the proposition E in the quantum state rho (a statistical operator). It is pointed out that EF=FE implies/implied by For all rho :p(E.F, rho )=p(F.E, rho ), EF=E implies/implied by For all rho : p(E.F, rho )=p(E, rho ), and EF=0 implies/implied by For all rho :p(E.F, rho )=0. Proof is given for generalisations of these simple characterisations to arbitrary strings (products of operators) and chains (of filters). Other cases of parallelism between strings and chains and departure from it are also studied.

Variational analysis of rotating neutron stars

The variational method of Nauenberg and Chapline is generalized to obtain explicit but approximate formulae for the total mass, baryon number, and angular momentum of slowly rotating neutron stars. The trial configurations employed have uniform density and angular velocity (as measured locally by zero-angular-momentum observers), but an arbitrary zero-entropy equation of state rho=rho (n). It is found that rotation can increase the pressure in a body which is sufficiently relativistic. (AIP)