Yes I am thinking of aniewrsng to Frank since for the first time in my life it seems that my collaborators and I are on the brink of a very big result. Might tell you what we found, but probably equally interesting is how all this happened. I am still baffled by the how . I will try to summarize in a few lines what and how.What we did is to solve a 60 years old problem called the Fermion Minus Sign Problem. To understand, one must go back to the foundations of quantum mechanics. There are two types of elementary particles ; one type is called bosons [ From the indian physicist Bose] and the other type is called fermions [ form the italian-american physicist Enrico Fermi, one of my all time heros]. What distinguishes them is their properties where they start to interact. If you put two bosons together and make one turn around the other [ physically turn, I mean], then nothing happens. Their wave function [ which is the object carrying all the information about them] is unperturbed. They can dance like this as much as they want, the information they cary is unchanged. You find bosons everywhere ; they are the quanta of lights, or photons, they are the quanta of vibrations in a slid, or phonons, they are the elementary particles carrying current in a superconductor, called Cooper pairs. Since we are bathing in light, we can say that we are bathing in a see of bosons [ sure you are happy to know this !]Now it’s no the end of the story. Another kind of elementary particle is present : the fermions. Those have the property that when one is turning around another, the wave function changes sign. It is a bit as if they were getting dizzy by turning around another, and thus they get sick [ I love the anthropologic analogies, hope it is OK with you guys]. The consequences of this for many particles are drastic : they repel each other and refuse [ u to the Planck scale, which means that they refuse very very much] to occupy the same quantum state [ or to share the same information]. What happens is that in a slid, you have to pile up those particles into an incompressible bulk of states, so that each state is occupied only once. Those very individualistic beats are also not that mysterious, they are for example the electrons, and the protons, of the quarks. Typical metals for example, have electrons as the elementary carriers. Well, Enrico Fermi noticed, just after the war, that all the statistical algorithms used to simulate quantum behavior with fermions where taking infinite amount of time to converge. This is the due to the change of sign of the wave function. When an assembly of fermion sin put inside the computer, and a Monte Carlo Algorithm is used to simulate them, then the multiple exchange of positions of the particles, creates in the simulation a random b11 sign, which is impossible to sum up with reasonable accuracy. This was very annoying since many of the quantum physics open problems involves such fermions[ like high temperature superconductivity, or quantum Chromodynamics on a lattice, quarks confinement , for a few of them]. This is what we are on the brnk on solving [ it is 99 % sure now I woudl say] with my collaborator Konstantin Efetov and one of his student, the very brilliant Hendrik Meier. What we did is simply to describe any kind of system of fermions into a system of bosons. We just have found a away to pass systematically from one statistic t another, for any system of many particles.It is possible because if your couple two fermions together you create a boson imagine two fermions now turn around two fermions It is kind of a tour de force but kind of simple once we found it. You can write it in 10 lines, although with some subtlety between each line.For us it is 2 years of work, 100 pages of calculations which simplified over and over up to the 10 lines.We are currently checking the numerics, namely putting things in the computer and see whether the algorithm converges or not.So you are right it is lots of sweat, but 5 years ago we got with Kostya what I would call a miraculous week, where inspiration came over us. It is one of the most impressive event that happened to me, [ to us] and frankly, without it there would have been nothing. Our result is currently under intense debate in the community since people thought after 60 years this would not be possible anymore. I pass the sociology of it which is quite a nightmare. We got the support of the greatest Nobel Price [ and for me the greatest living physicist of the field] Philip Anderson,but there is as well a coalition against us blocking the publication of our papers for months, trying to steal the result etc we are blessed because at the end the numerical check will produce a black or white answer ; that’s the beauty of science. It is looking good, so I would be extremely surprised at this point if the answer was black. I can tell you more about what I call our miraculous week , but usually I don’t tell much about it. It is part of the sacred for me. Believe me Inspiration was almost palpable in the room, between Kostya and me.
