Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions

Pairing plays a crucial role in nuclear spectra and attempts to describe it has a long history in nuclear physics. The limiting case in which all single particle states are degenerate, but with different s-wave pairing strengths was only recently solved. In this strong coupling limit the nuclear pairing Hamiltonian also exhibits a supersymmetry. Another solution away from those limits, namely two non-degenerate single particle states with different pairing strengths, was also given. In this contribution these developments are summarized and difficulties with possible generalizations to more single particle states and d-wave pairing are discussed.Comment: 6 pages of LATEX, to be published in the Proceedings of the "10th Int. Spring Seminar on Nuclear Physics: New Quests in Nuclear Structure", Vietri Sul Mare, May 21-25, 201

Localized collective excitations in doped graphene in strong magnetic fields

We consider collective excitations in graphene with filled Landau levels (LL’s) in the presence of an external potential due to a single charged donor D+ or acceptor A− impurity. We show that localized collective modes split off the magnetoplasmon continuum and, in addition, quasibound states are formed within the continuum. A study of the evolution of the strengths and energies of magneto-optical transitions is performed for integer filling factors ν=1,2,3,4 of the lowest LL. We predict impurity absorption peaks above as well as below the cyclotron resonance. We find that the single-particle electron-hole symmetry of graphene leads to a duality between the spectra of collective modes for the D+ and A−. The duality shows up as a set of the D+ and A− magnetoabsorption peaks having the same energies but active in different circular polarizations

Inclusive b and b anti-b production with quasi-multi-Regge kinematics at the Tevatron

We consider b-jet hadroproduction in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in t-channel exchanges at high energies. The preliminary data on inclusive b-jet and b anti-b-dijet production taken by the CDF Collaboration at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive b-jet production to be the scattering of a Reggeized gluon and a Reggeized b-quark to a b quark, which is described by the effective Reggeon-Reggeon-quark vertex. The main contribution to b anti-b-pair production arises from the scattering of two Reggeized gluons to a b anti-b pair, which is described by the effective Reggeon-Reggeon-quark-quark vertex. Our anaysis is based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions using as input the Martin-Roberts-Stirling-Thorne collinear parton distribution functions of the proton.Comment: 14 pages, 4 figures; formulas for effective vertices included, discussion of errors somewhat expanded; accepted for publication in Phys. Rev.

Supersymmetry and Nuclear Pairing

We show that nuclear pairing Hamiltonian exhibits supersymmetry in the strong-coupling limit. The underlying supersymmetric quantum mechanical structure explains the degeneracies between the energies of the N and Nmax-N+1 pair eigenstates. The supersymmetry transformations connecting these states are given.Comment: 4 pages of REVTEX, one figur

A System Exhibiting Toroidal Order

A two dimensional system of discs upon which a triangle of spins are mounted is shown to undergo a sequence of interesting phase transitions as the temperature is lowered. We are mainly concerned with the `solid' phase in which bond orientational order but not positional order is long ranged. As the temperature is lowered in the `solid' phase, the first phase transition involving the orientation or toroidal charge of the discs is into a `gauge toroid' phase in which the product of a magnetic toroidal parameter and an orientation variable (for the discs) orders but due to a local gauge symmetry these variables themselves do not individually order. Finally, in the lowest temperature phase the gauge symmetry is broken and toroidal order and orientational order both develop. In the `gauge toroidal' phase time reversal invariance is broken and in the lowest temperature phase inversion symmetry is also broken. In none of these phases is there long range order in any Fourier component of the average spin. A definition of the toroidal magnetic moment $T_i$ of the $i$th plaquette is proposed such that the magnetostatic interaction between plaquettes $i$ and $j$ is proportional to $T_iT_j$. Symmetry considerations are used to construct the magnetoelectric free energy and thereby to deduce which coefficients of the linear magnetoelectric tensor are allowed to be nonzero. In none of the phases does symmetry permit a spontaneous polarization.Comment: 9 pages, 6 figure

Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations

The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studies for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax function is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has vanishing determinant. Frobenius manifolds provide a natural setting in which to study the bi-Hamiltonian structure of certain classes of hydrodynamic systems. Some ideas on how this structure may be extanded to include degenerate bi-Hamiltonian structures, such as those given in the first part of the paper, are given.Comment: 28 pages, LaTe

Classical Polylogarithms for Amplitudes and Wilson Loops

We present a compact analytic formula for the two-loop six-particle MHV remainder function (equivalently, the two-loop light-like hexagon Wilson loop) in N = 4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Li_k with cross-ratios of momentum twistor invariants as their arguments. In deriving our result we rely on results from the theory of motives.Comment: 11 pages, v2: journal version, minor corrections and simplifications, additional details available at http://goo.gl/Cl0

Parametric downconversion with optimized spectral properties in nonlinear photonic crystals

We study the joint spectral properties of photon pairs generated by spontaneous parametric down-conversion in a one-dimensional nonlinear photonic crystal in a collinear, degenerate, type-II geometry. We show that the photonic crystal properties may be exploited to compensate for material dispersion and obtain photon pairs that are nearly factorable, in principle, for arbitrary materials and spectral regions, limited by the ability to fabricate the nonlinear crystal with the required periodic variation in the refractive indices for the ordinary and extraordinary waves.Comment: 9 pages, 6 figure