Quantum Unique Ergodicity for maps on the torus

When a map is classically uniquely ergodic, it is expected that its quantization will posses quantum unique ergodicity. In this paper we give examples of Quantum Unique Ergodicity for the perturbed Kronecker map, and an upper bound for the rate of convergence.Comment: 17 pages Added a construction of non diophantine irrationals with arbitrary slow rate of convergenc

CHANGES IN MEXICAN AGRICULTURAL POLICIES, 2001-2003

Several changes in agricultural policies in Mexico have taken place during the administration of President Fox, which started in December 2000. For the fist time in modern history an opposition party won the Presidential election in July of that year. The new government has shown a new attitude towards agriculture, seeing to the greatest possible extent market oriented policies and is pushing hard to change the attitude of Mexican farmers, in order to foster their entrepreneurial skills. Traditionally most farmers have relied heavily in government guidance for their production and marketing decisions. In contrast, the largest farmer organizations, with strong political ties to the former governing Party, do not share a large the new policy orientations. Moreover, the Fox administration does not hold a majority in Congress. Even though all political parties state that agriculture is one of their main priorities, a common view is lacking. Policy developments during the last two years should be analyzed under the perspective of compromise between the major players involved.Agricultural and Food Policy,

Scarred eigenstates for arithmetic toral point scatterers

We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the standard tori $\mathbb{R}^d/2 \pi\mathbb{Z}^d$ in dimensions $d=2,3$. Despite quantum ergodicity holding for the set of "new" eigenfunctions we show that there is scarring in the momentum representation for $d=2,3$, as well as in the position representation for $d=2$ (i.e., the eigenfunctions fail to equidistribute in phase space along an infinite subsequence of new eigenvalues.) For $d=3$, scarred eigenstates are quite rare, but for $d=2$ scarring in the momentum representation is very common --- with $N_{2}(x) \sim x/\sqrt{\log x}$ denoting the counting function for the new eigenvalues below $x$, there are $\gg N_{2}(x)/\log^A x$ eigenvalues corresponding to momentum scarred eigenfunctions.Comment: 31 pages, 1 figur

The Galois group of random elements of linear groups

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over F. We show that the structure of Gal(F(g)/ F) has a typical behaviour depending on F, and on the geometry of the Zariski closure of \Gamma (but not on \Gamma)

MEXICAN AGRICULTURAL TRADE UNDER NAFTA: AN ASSESSMENT AFTER FIVE YEARS OF IMPLEMENTATION

International Relations/Trade,