709 research outputs found
Hermitian Young Operators
Starting from conventional Young operators we construct Hermitian operators
which project orthogonally onto irreducible representations of the (special)
unitary group.Comment: 15 page
Quantum number projection at finite temperature via thermofield dynamics
Applying the thermo field dynamics, we reformulate exact quantum number
projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit
formulae are derived for the simultaneous projection of particle number and
angular momentum, in parallel to the zero-temperature case. We also propose a
practical method for the variation-after-projection calculation, by
approximating entropy without conflict with the Peierls inequality. The quantum
number projection in the finite-temperature mean-field theory will be useful to
study effects of quantum fluctuations associated with the conservation laws on
thermal properties of nuclei.Comment: 27 pages, using revtex4, to be published in PR
Hard sphere crystallization gets rarer with increasing dimension
We recently found that crystallization of monodisperse hard spheres from the
bulk fluid faces a much higher free energy barrier in four than in three
dimensions at equivalent supersaturation, due to the increased geometrical
frustration between the simplex-based fluid order and the crystal [J.A. van
Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here,
we analyze the microscopic contributions to the fluid-crystal interfacial free
energy to understand how the barrier to crystallization changes with dimension.
We find the barrier to grow with dimension and we identify the role of
polydispersity in preventing crystal formation. The increased fluid stability
allows us to study the jamming behavior in four, five, and six dimensions and
compare our observations with two recent theories [C. Song, P. Wang, and H. A.
Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in
press (2009)].Comment: 15 pages, 5 figure
Free Fermions and Thermal AdS/CFT
The dynamics of finite temperature U(N) gauge theories on can be
described, at weak coupling, by an effective unitary matrix model. Here we
present an exact solution to these models, for any value of , in terms of a
sum over representations. Taking the large limit of this solution provides
a new perspective on the deconfinement transition which is supposed to be dual
to the Hawking-Page transition. The large phase transition manifests itself
here in a manner similar to the Douglas-Kazakov phase transition in 2d
Yang-Mills theory. We carry out a complete analysis of the saddle
representation in the simplest case involving only the order parameter . We find that the saddle points corresponding to thermal , the small
black hole and the large black hole can all be described in terms of free
fermions. They all admit a simple phase space description {\it a la} the BPS
geometries of Lin, Lunin and Maldacena.Comment: (0+34) pages and 9 figures, v2 references adde
Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble
We set up recursion relations for the partition function and the ground-state
occupancy for a fixed number of non-interacting bosons confined in a square box
potential and determine the temperature dependence of the specific heat and the
particle number in the ground state. A proper semiclassical treatment is set up
which yields the correct small-T-behavior in contrast to an earlier theory in
Feynman's textbook on Statistical Mechanics, in which the special role of the
ground state was ignored. The results are compared with an exact quantum
mechanical treatment. Furthermore, we derive the finite-size effect of the
system.Comment: 18 pages, 8 figure
Correlation functions in a c=1 boundary conformal field theory
We obtain exact results for correlation functions of primary operators in the
two-dimensional conformal field theory of a scalar field interacting with a
critical periodic boundary potential. Amplitudes involving arbitrary bulk
discrete primary fields are given in terms of SU(2) rotation coefficients while
boundary amplitudes involving discrete boundary fields are independent of the
boundary interaction. Mixed amplitudes involving both bulk and boundary
discrete fields can also be obtained explicitly. Two- and three-point boundary
amplitudes involving fields at generic momentum are determined, up to
multiplicative constants, by the band spectrum in the open-string sector of the
theory.Comment: 33 pages, 6 figure
Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields
We calculate the energy band structure for electrons in an external periodic
potential combined with a perpendicular magnetic field. Electron-electron
interactions are included within a Hartree approximation. The calculated energy
spectra display a considerable degree of self-similarity, just as the
``Hofstadter butterfly.'' However, screening affects the butterfly, most
importantly the bandwidths oscillate with magnetic field in a characteristic
way. We also investigate the dynamic response of the electron system in the
far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can
be interpreted mainly in semiclassical terms, while others originate from
inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and
graphicx styles. Accepted for publication in PRB Brief Report
The Impact of Sectoral Minimum Wage Laws on Employment, Wages and Hours of Work in South Africa
This paper attempts to investigate the impact of sectoral wage laws in South Africa. Specifically, we examine the impact of minimum wage laws promulgated in the Retail, Domestic work, Forestry, Security, and Taxi sectors using 15 waves of biannual Labour Force Survey data for the 2000-2007 period
Boundary Conformal Field Theory and Ribbon Graphs: a tool for open/closed string dualities
We construct and fully characterize a scalar boundary conformal field theory
on a triangulated Riemann surface. The results are analyzed from a string
theory perspective as tools to deal with open/closed string dualities.Comment: 40 pages, 7 figures; typos correcte
A Hexagonal Theory of Flavor
We construct a supersymmetric theory of flavor based on the discrete gauge
group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under
proper rotations in three dimensions. The representation structure of the group
allows one to distinguish the third from the lighter two generations of matter
fields, so that in the symmetry limit only the top quark Yukawa coupling is
allowed and scalar superpartners of the first two generations are degenerate.
Light fermion Yukawa couplings arise from a sequential breaking of the flavor
symmetry, and supersymmetric flavor-changing processes remain adequately
suppressed. We contrast our model with others based on non-Abelian discrete
gauge symmetries described in the literature, and discuss the challenges in
constructing more minimal flavor models based on this approach.Comment: 19 pages, ReVTeX, 1 eps figur
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