Grassmann Variables and the Jaynes-Cummings Model

This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the two level atom) can be used to treat the Jaynes-Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker-Planck equation involving both left and right Grassmann differentiation can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, where the correspondence rules for bosonic operators are non-standard and hence the Fokker-Planck equation is also unusual. Initial conditions, such as for initially uncorrelated states, are used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enables the six coupled equations for the new c-number functions (also equivalent to the canonical Grassmann distribution function) to be solved analytically, based on an ansatz from a 1980 paper by Stenholm. It is then shown that the distribution function is the same as that determined from the well-known solution based on coupled equations for state vector amplitudes of atomic and n-photon product states. The treatment of the simple two fermion mode Jaynes-Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for multi-mode fermionic applications in quantum-atom optics.Comment: 57 pages, 0 figures. Version

Usage Pattern Recognition in Student Activities

Proceedings of: 6th European Conference of Technology Enhanced Learning, EC-TEL 2011, Palermo, Italy, September 20-23, 2011.This paper presents an approach of collecting contextualized attention metadata combined from inside as well as outside a LMS and analyzing them to create feedback about the student activities for the teaching staff. Two types of analyses were run on the collected data: first, key actions were extracted to identify usage patterns and tendencies throughout the whole course and then usage statistics and patterns were identified for some key actions in more detail. Results of both analyses were visualized and presented to the teaching staff for evaluation.The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007- 2013) under grant agreement no 231396 (ROLE project). Work was also partially funded by the Learn3 project (TIN2008-05163/TSI), the eMadrid project (S2009/TIC-1650), and the Acción Integrada DE2009-0051

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version of the pape

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

Asymptotic safety of simple Yukawa systems

We study the triviality and hierarchy problem of a Z_2-invariant Yukawa system with massless fermions and a real scalar field, serving as a toy model for the standard-model Higgs sector. Using the functional RG, we look for UV stable fixed points which could render the system asymptotically safe. Whether a balancing of fermionic and bosonic contributions in the RG flow induces such a fixed point depends on the algebraic structure and the degrees of freedom of the system. Within the region of parameter space which can be controlled by a nonperturbative next-to-leading order derivative expansion of the effective action, we find no non-Gaussian fixed point in the case of one or more fermion flavors. The fermion-boson balancing can still be demonstrated within a model system with a small fractional flavor number in the symmetry-broken regime. The UV behavior of this small-N_f system is controlled by a conformal Higgs expectation value. The system has only two physical parameters, implying that the Higgs mass can be predicted. It also naturally explains the heavy mass of the top quark, since there are no RG trajectories connecting the UV fixed point with light top masses.Comment: 14 pages, 3 figures, v2: references added, typos corrected, minor numerical correction

Digestion and energy value of macerated sudangrass hay used in growing-finishing diets for feedlot cattle

Mechanical maceration enhances site and extent of digestion of low-moisture, low-quality forages. Four Holstein steers (172 ± 8 kg) with cannulas in rumen and proximal duodenum were used in 4x4 Latin square design to evaluate the process of mechanical maceration of sudangrass hay on the characteristics of ruminal and total tract digestion. Treatments consisted of a steam-flaked corn-based growing diet supplemented with 21 % forage (DM basis) as: i) wheat straw (Triticum aestivum, STRW), ii) sudangrass hay (Sorghum sudanense, SG), iii) macerated SG at intensity of 4,134 kPa (MAC600) and 4) macerated SG at intensity of 6,200 kPa (MAC900). All forages were ground to pass through a 3.8 cm screen before incorporation into complete mixed diets (21:79 forage to concentrate ratio). Maceration did not affect (p ≥ 0.17) on site and extent of OM, N and ADF, and DE of sudangrass supplemented diets. Characteristics of ruminal digestion of OM, ADF, starch, as well as, microbial efficiency (microbial N, g kg-1 of OM fermentad) and protein efficiency (nonammonia N, g g-1 of N intake) were not different (p ≥ 0.11) for wheat straw versus sudangrass supplemented diets. However, total tract digestion of OM, ADF, N, and DE diet were greater (p ≤ 0.05) for sudangrass than for wheat straw supplemented diets. Using the replacement technique, DE value of SG averaged 9.59 MJ kg-1, very close to the expected value given its chemical composition. Mechanical maceration did not enhance the feeding value of sudangrass hay. Increase the intensity of maceration from 4,134 to 6,200 kPa did not altered ruminal or total tract digestion of OM, NDF or energy value of processed ha