In the quantum world of the crack, one concept that needs a place at the table is Luttinger liquids.
This concept has recently been established as a fundamental paradigm vital to our understanding of the properties of one-dimensional quantum systems, which has only recently led to a number of theoretical breakthroughs in understanding how electrons behave in the one-dimensional world. To expand the explanation, in our everyday real life experience, we live in a three-dimensional world. Phenomena in a world of the crack with only one spatial dimension may appear an esoteric subject, and for a long time it was perceived as such. But today, this is changing as our knowledge of matter’s inner atomic structure has evolved. It appears that in many real-life materials a chain-like pattern of overlapping atomic orbitals leaves electrons belonging on these orbitals with only one dimension where they can freely travel. With the nano-patterned microchips and nano-wires heading into consumer electronics, the question “how do electrons behave in one dimension?” is no longer a theoretical playground but something that a curious mind might ask when thinking of how his or her computer works. One-dimensional problems being mathematically simpler, a number of exact solutions describing “model” one-dimensional systems were known to theorists for years. Only recently has the conformal field theory of the constrained dimensional movement of the electron been consolidated and experimentally verified. Our past knowledge has now been put together like the pieces of a jigsaw puzzle and predicts remarkable universal critical behavior for one-dimensional systems. The world of one dimension is full of surprises that we can readily appreciate if we can use our imaginations The geometry of one dimension has its special rules and is more restrictive than we would imagine. In the one dimensional world, two objects cannot move past one another unless they can penetrate each other; the one on the right will always remain on the right, and the one on the left will always be on the left. Hence, a clear distinction between the two fundamental types of particles, those obeying Bose and Fermi statistics, disappears in the one-dimensional world. Indeed, the difference between bosons and fermions comes into play in quantum mechanics when two particles swap places. This has no effect for the system of bosons but changes the sign of the wave function for fermions. If particles never swap places, the system’s descriptions in terms of Bose and Fermi elementary excitations are equally legitimate, the choice being just a matter of convenience as the non-interacting fermions are equivalent to strongly interacting bosons and vice versa. The one dimensional quantum field theory theorists have developed a new technique known as “bosonisation” which provides a unified description of the one-dimensional world of the electron. When cracks develop on the surface of metals, we enter the world of one dimensional electron flow were bosonisation and Luttinger liquid theory apply. Furthermore, Fermi-liquid accurately predicts the properties of “usual”, three-dimensional metals, but fails dramatically in one dimension. In the volume in and immediate around the crack, we must use the new concept of a Luttinger liquid to understand the way electrons behave. A Luttinger liquid theory predicts universal properties for the great variety of one dimensional systems, including the electronic states of carbon nanotubes and nanowires, conducting properties of conjugated polymers and fluid behavior of Bose liquids confined within one dimensional nano-capillaries. The simplest and best studied example of the Luttinger liquid is a chain of quantum spins ½ where the energy depends on the misalignment of the nearest neighbors. The detection of superconductive behavior in and around cracks by Miley might be understood as a consequence of the “bosonisation” of electrons due to the one dimensional electron flow were electrons become ballistic and can ignore impurities that would usually restrict electron flow in three dimensions. I believe that this appearance of superconductive behavior of electron flow is an important clue to the one dimensional nature of electron behavior in and around the crack that Ed Storms is addressing. Cheers: Axil On Sun, Jun 10, 2012 at 2:53 PM, Eric Walker <eric.wal...@gmail.com> wrote: > On Sun, Jun 10, 2012 at 7:49 AM, Jojo Jaro <jth...@hotmail.com> wrote: > >> >> Ed calculates that the energy of formation for a neutron is 0.76MeV. >> This energy must be concentrated from a "sea" of energy less than 0.1 eV. >> > > Not necessarily. That's only one of several approaches. > > Suppose you have a crack that serves as an antenna, along the lines Lou > has suggested. Now add a soup of free electrons in the vicinity of the > crack (a plasmon). Now bring in a cosmic ray or a gamma ray from an > earlier event. The high-energy incoming photon does something funny with > the crack and the plasmon, and perhaps as with a lightning bolt or a staple > gun, a free proton in the area is zapped (with a loud crackle, one > imagines). There you have all the energy needed to create a neutron. No > need for a magical localization of energy from a low-energy environment. > > Eric > >
