Maxon and roton measurements in nanoconfined 4^4He

We investigate the behavior of the collective excitations of adsorbed $^4$He in an ordered hexagonal mesopore, examining the crossover from a thin film to a confined fluid. Here we present the inelastic scattering results as a function of filling at constant temperature. We find a monotonic transition of the maxon excitation as a function of filling. This has been interpreted as corresponding to an increasing density of the adsorbed helium, which approaches the bulk value as filling increases. The roton minimum exhibits a more complicated behavior that does not monotonically approach bulk values as filling increases. The full pore scattering resembles the bulk liquid accompanied by a layer mode. The maxon and roton scattering, taken together, at intermediate fillings does not correspond to a single bulk liquid dispersion at negative, low, or high pressure.Comment: 9 pages, 10 figure

Is simultaneous yy and ξ\xi--scaling in the quasi-elastic region accidental?

We study the $y$ and $\xi$--scaling of the nuclear response at large momentum transfer in order to understand how scaling based on very different descriptions of the elementary interaction can occur simultaneously. We find that the approximate validity of $\xi$-scaling at low energy loss arises from the coincidental behavior of the quasielastic and deep inelastic cross sections.Comment: 4 pages, 3 Postscript figure

Down The Rabbit Hole: A look at integrating classic literature into a secondary mathematics curriculum

The importance of mathematics and reading is paramount to the advancement of civilization. Research has shown that mathematics and reading, along with writing, have a strong correlation. The new Common Core State Standards (CCSS) in mathematics stress the importance of applying mathematical concepts to other subjects and real life. Interestingly, the mathematics and English curriculums have some objectives in common. Classic literature provides a unique context for mathematical concepts to be applied. Using classic literature to teach mathematics could allow students to engage in mathematics and literature more deeply. Example lessons and worksheets supported by research allow teachers to another avenue to assist student in the learning of mathematics. The two lessons provided include examples that are derived from Alice’s Adventures in Wonderland and Through the Looking Glass written by Lewis Carroll. The lessons focus on a mix between teacher and student centered models. The first lesson is on using Venn diagrams. The second lesson is on the construction of truth tables

Direct mapping of the finite temperature phase diagram of strongly correlated quantum models

Optical lattice experiments, with the unique potential of tuning interactions and density, have emerged as emulators of nontrivial theoretical models that are directly relevant for strongly correlated materials. However, so far the finite temperature phase diagram has not been mapped out for any strongly correlated quantum model. We propose a remarkable method for obtaining such a phase diagram for the first time directly from experiments using only the density profile in the trap as the input. We illustrate the procedure explicitly for the Bose Hubbard model, a textbook example of a quantum phase transition from a superfluid to a Mott insulator. Using "exact" quantum Monte Carlo simulations in a trap with up to $10^6$ bosons, we show that kinks in the local compressibility, arising from critical fluctuations, demarcate the boundaries between superfluid and normal phases in the trap. The temperature of the bosons in the optical lattice is determined from the density profile at the edge. Our method can be applied to other phase transitions even when reliable numerical results are not available.Comment: 12 pages, 5 figure