Open problems in nuclear density functional theory

This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.Comment: 10 page

Competing interactions in the XYZ model

We study the interplay between a XY anisotropy $\gamma$, exchange modulations and an external magnetic field along the z direction in the XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in the space of couplings which occur due to competing relevant perturbations which are present. More general situations are also discussed.Comment: 6 pages, 6 figure

Lattice methods and the nuclear few- and many-body problem

We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.Comment: 20 pages, 3 figures, Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: (\vec \nabla \rho_p- \vec \nabla \rho_n)^2 G_d(\rho)+ (\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec J_p-\vec J_n) G_{so(\rho)+(\vec J_p-\vec J_n)^2 G_J(\rho) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1\pi$-exchange, iterated $1\pi$-exchange, and irreducible $2\pi$-exchange with intermediate $\Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(\rho)$, $G_{so}(\rho)$ and $G_J(\rho)$ which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.Comment: 12 pages, 5 figure

Occurrence of testicular microlithiasis in androgen insensitive hypogonadal mice

<b>Background</b>: Testicular microliths are calcifications found within the seminiferous tubules. In humans, testicular microlithiasis (TM) has an unknown etiology but may be significantly associated with testicular germ cell tumors. Factors inducing microlith development may also, therefore, act as susceptibility factors for malignant testicular conditions. Studies to identify the mechanisms of microlith development have been hampered by the lack of suitable animal models for TM.<BR/> <b>Methods</b>: This was an observational study of the testicular phenotype of different mouse models. The mouse models were: cryptorchid mice, mice lacking androgen receptors (ARs) on the Sertoli cells (SCARKO), mice with a ubiquitous loss of androgen ARs (ARKO), hypogonadal (hpg) mice which lack circulating gonadotrophins, and hpg mice crossed with SCARKO (hpg.SCARKO) and ARKO (hpg.ARKO) mice.<BR/> <b>Results</b>: Microscopic TM was seen in 94% of hpg.ARKO mice (n=16) and the mean number of microliths per testis was 81 +/- 54. Occasional small microliths were seen in 36% (n=11) of hpg testes (mean 2 +/- 0.5 per testis) and 30% (n=10) of hpg.SCARKO testes (mean 8 +/- 6 per testis). No microliths were seen in cryptorchid, ARKO or SCARKO mice. There was no significant effect of FSH or androgen on TM in hpg.ARKO mice.<BR/> <b>Conclusions</b>: We have identified a mouse model of TM and show that lack of endocrine stimulation is a cause of TM. Importantly, this model will provide a means with which to identify the mechanisms of TM development and the underlying changes in protein and gene expression

Correlation functions for 1d interacting fermions with spin-orbit coupling

We compute correlation functions for one-dimensional electron systems which spin and charge degrees of freedom are coupled through spin-orbit coupling. Charge density waves, spin density waves, singlet- triplet- superconducting fluctuations are studied. We show that the spin-orbit interaction modify the exponents and the phase diagram of the system, changing the dominant fluctuations and making new susceptibilities diverge for low temperature.Comment: 5 pages, 3 figures. Accepted for publication in Phys. Rev.

Instabilities in Luttinger liquids

We discuss the appearance of magnetic and charge instabilities, named respectively metamagnetism (MM) and phase separation (PS), in systems which can be described by a perturbed Luttinger liquid. We argue that such instabilities can be associated with the vanishing of the effective Fermi velocity v, which in some cases coincides with a divergence of the effective Luttinger parameter K. We analyze in particular an XXZ chain with next-nearest-neighbor interactions in different limits where MM shows up and an extended Hubbard model where in turn, PS occurs. Qualitative agreement with previous studies is found.Comment: 7 pages, 3 figure

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap

Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene

We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2)XU(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry.Comment: 35 page

Artificial graphene as a tunable Dirac material

Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.Comment: Review article, 14 pages, 5 figures, 112 Reference