7,021 research outputs found
Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio
A comparison of two magnetic ultra-cold neutron trapping concepts using a Halbach-octupole array
This paper describes a new magnetic trap for ultra-cold neutrons (UCNs) made
from a 1.2 m long Halbach-octupole array of permanent magnets with an inner
bore radius of 47 mm combined with an assembly of superconducting end coils and
bias field solenoid. The use of the trap in a vertical, magneto-gravitational
and a horizontal setup are compared in terms of the effective volume and
ability to control key systematic effects that need to be addressed in high
precision neutron lifetime measurements
Magnon Dispersion and Anisotropies in SrCu(BO)
We study the dispersion of the magnons (triplet states) in
SrCu(BO) including all symmetry-allowed Dzyaloshinskii-Moriya
interactions. We can reduce the complexity of the general Hamiltonian to a new
simpler form by appropriate rotations of the spin operators. The resulting
Hamiltonian is studied by both perturbation theory and exact numerical
diagonalization on a 32-site cluster. We argue that the dispersion is dominated
by Dzyaloshinskii-Moriya interactions. We point out which combinations of these
anisotropies affect the dispersion to linear-order, and extract their
magnitudes.Comment: 11 pages, 7 figures, 1 table, v2 conclusion shortened, figs clarifie
Random walks near Rokhsar-Kivelson points
There is a class of quantum Hamiltonians known as
Rokhsar-Kivelson(RK)-Hamiltonians for which static ground state properties can
be obtained by evaluating thermal expectation values for classical models. The
ground state of an RK-Hamiltonian is known explicitly, and its dynamical
properties can be obtained by performing a classical Monte Carlo simulation. We
discuss the details of a Diffusion Monte Carlo method that is a good tool for
studying statics and dynamics of perturbed RK-Hamiltonians without time
discretization errors. As a general result we point out that the relation
between the quantum dynamics and classical Monte Carlo simulations for
RK-Hamiltonians follows from the known fact that the imaginary-time evolution
operator that describes optimal importance sampling, in which the exact ground
state is used as guiding function, is Markovian. Thus quantum dynamics can be
studied by a classical Monte Carlo simulation for any Hamiltonian that is free
of the sign problem provided its ground state is known explicitly.Comment: 12 pages, 9 figures, RevTe
Quantum Deconstruction of 5D SQCD
We deconstruct the fifth dimension of 5D SCQD with general numbers of colors
and flavors and general 5D Chern-Simons level; the latter is adjusted by adding
extra quarks to the 4D quiver. We use deconstruction as a non-stringy UV
completion of the quantum 5D theory; to prove its usefulness, we compute
quantum corrections to the SQCD_5 prepotential. We also explore the
moduli/parameter space of the deconstructed SQCD_5 and show that for |K_CS| <
N_F/2 it continues to negative values of 1/(g_5)^2. In many cases there are
flop transitions connecting SQCD_5 to exotic 5D theories such as E0, and we
present several examples of such transitions. We compare deconstruction to
brane-web engineering of the same SQCD_5 and show that the phase diagram is the
same in both cases; indeed, the two UV completions are in the same universality
class, although they are not dual to each other. Hence, the phase structure of
an SQCD_5 (and presumably any other 5D gauge theory) is inherently
five-dimensional and does not depends on a UV completion.Comment: LaTeX+PStricks, 108 pages, 41 colored figures. Please print in colo
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