Mesoscopic interference

We analyze a double-slit experiment when the interfering particle is "mesoscopic" and one endeavors to obtain Welcher Weg information by shining light on it. We derive a compact expression for the visibility of the interference pattern: coherence depends on both the spatial and temporal features of the wave function during its travel to the screen. We set a bound on the temperature of the mesoscopic particle in order that its quantum mechanical coherence be maintained.Comment: 16 pages, 14 figure

Wigner function and coherence properties of cold and thermal neutrons

We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A "decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.Comment: 6 pages, 3 figures. Contribution to the Sixth Central-European Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May 199

Decoherence vs entropy in neutron interferometry

We analyze the coherence properties of polarized neutrons, after they have interacted with a magnetic field or a phase shifter undergoing different kinds of statistical fluctuations. We endeavor to probe the degree of disorder of the distribution of the phase shifts by means of the loss of quantum mechanical coherence of the neutron. We find that the notion of entropy of the shifts and that of decoherence of the neutron do not necessarily agree. In some cases the neutron wave function is more coherent, even though it has interacted with a more disordered medium.Comment: 13 pages, 5 figure

Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?

An n-town, for a natural number n, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form is known. We show that optimal n-towns can be computed in O(n^7.5) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.Comment: 26 pages, 6 figures, to appear in Computational Geometry: Theory and Application

Discrepância posterior e sua relação com o padrão de crescimento facial hiperdivergente

Poster apresentado na XXVII Reunião Científica Anual da SPODF. Figueira da Foz, 23-25 Abril 201