2 2 Ju l 2 00 5 TOPOLOGICAL MIXING FOR SUBSTITUTIONS ON TWO LETTERS
نویسندگان
چکیده
We investigate topological mixing for Z and R actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue θ2 of the substitution matrix satisfies |θ2| 6= 1. If |θ2| < 1, then (as is well-known) the substitution system is not topologically weak mixing, so it is not topologically mixing. We prove that if |θ2| > 1, then topological mixing is equivalent to topological weak mixing, which has an explicit arithmetic characterization. The case |θ2| = 1 is more delicate, and we only obtain some partial results.
منابع مشابه
2 4 Ju n 20 04 TOPOLOGICAL MIXING FOR SUBSTITUTIONS ON TWO LETTERS
We investigate topological mixing for Z and R actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue θ2 of the substitution matrix satisfies |θ2| 6= 1. If |θ2| < 1, then (as is well-known) the substitution system is not topologically weak mixing, so it is not topologically mixing. We prove that if |θ2| > 1, then topological mixi...
متن کاملar X iv : q ua nt - p h / 03 07 15 5 v 1 2 2 Ju l 2 00 3 On topological and quantum mechanical entanglement
We explore the relation between topological and quantum mechanical entanglement. We first emphasize on the similarities and differences between these two concepts. Then we show that a proper context for making such a connection is via the braid group operators. We then provide some specific examples and calculate the entangling power of braid group operators. Although our results shows some pat...
متن کاملar X iv : a st ro - p h / 03 07 21 1 v 2 2 8 Ju l 2 00 3 Charged Domain Walls
In this paper we investigate Charged Domain Walls (CDW's), topological defects that acquire surface charge density Q induced by fermion states localized on the walls. The presence of an electric and magnetic field on the walls is also discussed. We find a relation in which the value of the surface charge density Q is connected with the existence of such topological defects.
متن کاملar X iv : h ep - p h / 01 07 17 5 v 1 1 6 Ju l 2 00 1 η - η ′ mixing in U ( 3 ) chiral perturbation theory 1
We investigate η-η ′ mixing in infrared regularized U (3) chiral perturbation theory by calculating the η and η ′ masses up to one-loop order. From this analysis it becomes obvious that even at leading order η-η ′ mixing does not obey the usually assumed one-mixing angle scheme if large N c counting rules are not employed.
متن کاملar X iv : m at h - ph / 0 50 70 67 v 1 2 7 Ju l 2 00 5 Improved mixing bounds for the Anti - Ferromagnetic Potts Model on Z 2 ∗
We consider the anti-ferromagnetic Potts model on the the integer lattice Z. The model has two parameters, q, the number of spins, and λ = exp(−β), where β is “inverse temperature”. It is known that the model has strong spatial mixing if q > 7 or if q = 7 and λ = 0 or λ > 1/8 or if q = 6 and λ = 0 or λ > 1/4. The λ = 0 case corresponds to the model in which configurations are proper q-colouring...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005