The Stern-Brocot tree (or rather half of it) can be defined as follows. Start with two fractions 0/1 and 1/1, forming an ordered set S0. (Throughout this paper, “fraction” means “fraction in lowest terms”.) At stage k, (k = 1, 2, . . .), form a new set Sk by inserting between each pair of adjacent fractions in Sk−1, say p/q and r/s, the fraction (p+r)/(q+s). Name the (ordered) set of fractions ...

Abstract: An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this arti...

Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A natural arithmetization of the theory is obtained by representing central and Christoffel words by irreducible fractions labeling respectively two binary trees, the Raney (or Calkin-Wilf) tree and the Stern-Brocot tree. ...

The ground state configurations of the one–dimensional Falicov–Kimball model are studied exactly with numerical calculations revealing unexpected effects for small interaction strength. In neutral systems we observe molecular formation, phase separation and changes in the conducting properties; while in non–neutral systems the phase diagram exhibits Farey tree order (Aubry sequence) and a devil...

We discuss the possibility of realizing a microscopic Stern--Gerlach magnet for electrons using counter-propagating bichromatic laser light. Absorption of two photons with frequency 0) combined with stimulated emission of one photon with frequency 2w allows for the conservation of energy, momentum, and angular momentum, The possibility of constructing such a device appears to be an open question,

At the LHC, top quark pairs are dominantly produced from gluons, making it difficult to measure the top quark forward-backward asymmetry. To improve the asymmetry measurement, we study variables that can distinguish between top quarks produced from quarks and those from gluons: the invariant mass of the top pair, the rapidity of the top-antitop system in the lab frame, the rapidity of the top q...