Renormalization of the Sigma-Omega model within the framework of U(1) gauge symmetry

It is shown that the Sigma-Omega model which is widely used in the study of nuclear relativistic many-body problem can exactly be treated as an Abelian massive gauge field theory. The quantization of this theory can perfectly be performed by means of the general methods described in the quantum gauge field theory. Especially, the local U(1) gauge symmetry of the theory leads to a series of Ward-Takahashi identities satisfied by Green's functions and proper vertices. These identities form an uniquely correct basis for the renormalization of the theory. The renormalization is carried out in the mass-dependent momentum space subtraction scheme and by the renormalization group approach. With the aid of the renormalization boundary conditions, the solutions to the renormalization group equations are given in definite expressions without any ambiguity and renormalized S-matrix elememts are exactly formulated in forms as given in a series of tree diagrams provided that the physical parameters are replaced by the running ones. As an illustration of the renormalization procedure, the one-loop renormalization is concretely carried out and the results are given in rigorous forms which are suitable in the whole energy region. The effect of the one-loop renormalization is examined by the two-nucleon elastic scattering.Comment: 32 pages, 17 figure

Does the 2D Hubbard Model Really Show d-Wave Superconductivity?

Some issues concerning the question if the two-dimensional Hubbard model really show d-wave superconductivity are briefly discussed.Comment: Revtex, no figure

Evaluating the use of a wiki for collaborative learning

A wiki is able to provide a learning environment which is closely aligned with the social‐constructivist approach and is more natural than many tools where open collaboration and the exchange of ideas are important. This case study analyses and evaluates essential aspects for the successful deployment of a wiki in a higher education setting using Salmon's five‐stage e‐learning framework. Indicators of the learning benefits were determined by qualitative analysis of students' wiki contributions. Students' perceptions were captured through interviews and questionnaires at the start and end of the project, thereby providing indicators of their motivation towards this method of learning. Our results suggest that a wiki can promote effective collaborative learning and confidence in formative self and peer assessment by facilitating rapid feedback, vicarious learning through observing others' contributions and easy navigation and tracking facilities. Student authorship was also encouraged. Issues identified included providing easy access to the wiki, lack of personalisation, possible vandalism and plagiarism. Also, students with learning difficulties might require extra help and take longer to familiarise themselves with this new e‐learning environment

Aharonov-Casher phase and persistent current in a polyacetylene ring

We investigate a polyacetylene ring in an axially symmetric, static electric field with a modified SSH Hamiltonian of a polyacetylene chain. An effective gauge potential of the single electron Hamiltonian due to spin-field interaction is obtained and it results in a Fr\"{o}hlich's type of superconductivity equivalent to the effect of travelling lattice wave. The total energy as well as the persistent current density are shown to be a periodic function of the flux of the gauge field embraced by the polyacetylene ring.Comment: 12 pages, 5 figure

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

Band Structure and Quantum Conductance of Nanostructures from Maximally-Localized Wannier Functions: The Case of Functionalized Carbon Nanotubes

We have combined large-scale, $\Gamma$-point electronic-structure calculations with the maximally-localized Wannier functions approach to calculate efficiently the band structure and the quantum conductance of complex systems containing thousands of atoms while maintaining full first-principles accuracy. We have applied this approach to study covalent functionalizations in metallic single-walled carbon nanotubes. We find that the band structure around the Fermi energy is much less dependent on the chemical nature of the ligands than on the $sp^3$ functionalization pattern disrupting the conjugation network. Common aryl functionalizations are more stable when paired with saturating hydrogens; even when paired, they still act as strong scattering centers that degrade the ballistic conductance of the nanotubes already at low degrees of coverage.Comment: To be published in Phys. Rev. Let

Cosmic ray feedback in the FIRE simulations: constraining cosmic ray propagation with GeV gamma ray emission

We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-$L\star$ starburst, and $L\star$ galaxies with different propagation models, including advection, isotropic and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two moment method. We forward-model and compare to observations of $\gamma$-ray emission from nearby and starburst galaxies. We reproduce the $\gamma$-ray observations of dwarf and $L\star$ galaxies with constant isotropic diffusion coefficient $\kappa \sim 3\times 10^{29}\,{\rm cm^{2}\,s^{-1}}$. Advection-only and streaming-only models produce order-of-magnitude too large $\gamma$-ray luminosities in dwarf and $L\star$ galaxies. We show that in models that match the $\gamma$-ray observations, most CRs escape low-gas-density galaxies (e.g.\ dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for $\gamma$-ray emissivities. Models where CRs are ``trapped'' in the star-forming disk have lower star formation efficiency, but these models are ruled out by $\gamma$-ray observations. For models with constant $\kappa$ that match the $\gamma$-ray observations, CRs form extended halos with scale heights of several kpc to several tens of kpc.Comment: 31 pages, 26 figures, accepted for publication in MNRA

Theory for Gossamer and Resonating Valence Bond Superconductivity

We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed gossamer superconductivity. We formulate a renormalized mean field theory to approximately take into account the strong correlation effect in the partially projected Gutzwiller wavefucntions. At the half filled, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a gossamer superconductor at small U. Away from the half filled,the Mott insulator is evolved into an resonating valence bond state, which is adiabatically connected to the gossamer superconductor.Comment: 10 pages, 13 figure

Sensing-Assisted Eavesdropper Estimation: An ISAC Breakthrough in Physical Layer Security

In this paper, we investigate the sensing-aided physical layer security (PLS) towards Integrated Sensing and Communication (ISAC) systems. A well-known limitation of PLS is the need to have information about potential eavesdroppers (Eves). The sensing functionality of ISAC offers an enabling role here, by estimating the directions of potential Eves to inform PLS. In our approach, the ISAC base station (BS) firstly emits an omnidirectional waveform to search for potential Eves’ directions by employing the combined Capon and approximate maximum likelihood (CAML) technique. Using the resulting information about potential Eves, we formulate secrecy rate expressions, which is a function of the Eves’ estimation accuracy. We then formulate a weighted optimization problem to simultaneously maximize the secrecy rate with the aid of the artificial noise (AN), and minimize the Cramér-Rao Bound (CRB) of targets’/Eves’ estimation. By taking the possible estimation errors into account, we enforce a beampattern constraint with a wide main beam covering all possible directions of Eves. This implicates that security needs to be enforced in all these directions. By improving estimation accuracy, the sensing and security functionalities provide mutual benefits, resulting in improvement of the mutual performances with every iteration of the optimization, until convergence. Our results avail of these mutual benefits and reveal the usefulness of sensing as an enabler for practical PLS