The explanation of the Fractional Quantum Hall Effect (FQHE)
The explanation of FQHE in view of Laughlin’s ideas is that there exist fillings (or, equivalently, magnetic field densities) at which the electron gas is particularly stable and condenses into a special ground state with high correlation. The slight deviations from these fillings result in quasi-particle excitations which carry fractional charge. As these excitations get pinned by the impurities and disorder present in the real samples, they do not contribute to the current. The conductance therefore does not change with the filling until the value of the filling for next stable ground state is reached. On Sat, Nov 14, 2015 at 9:51 AM, Bob Cook <frobertc...@hotmail.com> wrote: > Eric and Dave-- > > I agree with David’s assessment. In addition, since angular momentum must > be conserved, the effective circulation of electrons in a loop wants to > stay that way. Magnetic fields are much like electric fields—if > established and left alone, they remain unchanged. The charge does not > “evaporate” with time nor does it move because of the mass inertia > associated with it. The magnetic field does not change, because of the > angular momentum associated with it. Angular momentum and linear momentum > associated with inertia are very similar animals. They do not change > without cause--an expenditure or assumption of energy. > > Furthermore, from observation the angular momentum it only changes by a > certain discrete quanta. And charge only changes by discrete quanta—the > charge on an electron which goes from 0 to +l or –1 electron charge units. > Linear momentum of a particle seems to be uncontrolled and able to change > in any increment, no matter how small. However, it may eventually be found > to also be controlled at very small time increments and dimensions—those > associated with the Planck scale. > > That being said, a lot of people think that quarks exist with fractional > unit charges. I do not. Specifically I do not classify a quark as a > real division of charge, since they do not seem to exist by themselves. I > think that the suggestion fractional charges—quarks—are real is associated > with the necessary geometry of associated real charges in a group of close > electrons and positrons as occur in a nucleus. > > P. Hatt’s theory of the proton and and neutron as being constructed from > electrons and positrons seems a better fit to experimental reality than the > quark theory of the makeup of these large constituent particles. > > > Bob Cook > > *From:* David Roberson <dlrober...@aol.com> > *Sent:* Friday, November 13, 2015 10:25 PM > *To:* vortex-l@eskimo.com > *Subject:* Re: [Vo]: How many atoms to make condensed matter? > > Eric, replace the lossy magnet by a superconducting magnet and you get > the same result without requiring any additional work to be done. The loss > in the current carrying magnet is due to series resistance and if that > resistance is eliminated it would not require any additional power once the > current is set up. > > I consider electrons in orbits as being equivalent to a superconductor > current since the orbits do not collapse with time. No power is radiated > by an electron orbital and hence no work is required to keep it in the > proper location. > > Dave > > > > -----Original Message----- > From: Eric Walker <eric.wal...@gmail.com> > To: vortex-l <vortex-l@eskimo.com> > Sent: Fri, Nov 13, 2015 9:21 pm > Subject: Re: [Vo]: How many atoms to make condensed matter? > > Some of this thread has gotten to some of the basics relating to > magnetism, which is a bit of a mystery to me. There's the dynamic > magnetism that arises through a moving current. And there's the static > magnetism that is created through the formation of magnetic domains in a > ferromagnetic material, in which the spins of the atoms are aligned in one > or another direction. At a high level, these concepts make sense to me. > > What I don't fully understand is how conservation of energy applies in the > case of the system in this photo: > > http://i.imgur.com/YzC8KlI.jpg > > Here we have a strong permanent magnet and a keyring. They are configured > in an arrangement that, without the influence of the permanent magnetism, > would be unstable against the force of gravity. But the magnetism of the > magnet keeps the two components together in the assembly against gravity. > > A common explanation for this kind of thing will be something to the > effect that no work is being done in this system because there is no > movement. But I think that oversimplifies the mystery of it. We can > suspect that work is in fact being done at the atomic level if in our minds > we replace the permanent magnet with a magnet formed from a current > carrying wire wrapped around a piece of metal. We can set up a magnetic > field in this system by keeping current flowing through the wire, and we > must keep the current flowing in order to continue to have the field. We > could do that by turning a crank on a small hand generator or burning > petroleum to power an electrical generator. With the permanent magnet, one > suspects that there must be something comparable going on as well. > > My question is -- what is it that seems to be adding energy to the system > in order to keep the permanent magnetic field in place, analogous to the > motor with the crank or the electrical generator? What is the fuel in this > system that does the work? > > Eric > > > >
