4,289 research outputs found
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
The characteristic identity formalism discussed in our recent articles is
further utilized to derive matrix elements of type 2 unitary irreducible
modules. In particular, we give matrix element formulae for all
gl(m|n) generators, including the non-elementary generators, together with
their phases on finite dimensional type 2 unitary irreducible representations.
Remarkably, we find that the type 2 unitary matrix element equations coincide
with the type 1 unitary matrix element equations for non-vanishing matrix
elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424
Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
In this paper fundamental Wigner coefficients are determined algebraically by
considering the eigenvalues of certain generalized Casimir invariants. Here
this method is applied in the context of both type 1 and type 2 unitary
representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary
case are investigated. A symmetry relation between two classes of Wigner
coefficients is given in terms of a ratio of dimensions.Comment: 17 page
Cavity sideband cooling of a single trapped ion
We report a demonstration and quantitative characterization of
one-dimensional cavity cooling of a single trapped 88Sr+ ion in the resolved
sideband regime. We measure the spectrum of cavity transitions, the rates of
cavity heating and cooling, and the steady-state cooling limit. The cavity
cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the
moderate coupling between the ion and the cavity, are consistent with a simple
model [Phys. Rev. A 64, 033405] without any free parameters, validating the
rate equation model for cavity cooling.Comment: 5 pages, 4 figure
Tensor product representation of topological ordered phase: necessary symmetry conditions
The tensor product representation of quantum states leads to a promising
variational approach to study quantum phase and quantum phase transitions,
especially topological ordered phases which are impossible to handle with
conventional methods due to their long range entanglement. However, an
important issue arises when we use tensor product states (TPS) as variational
states to find the ground state of a Hamiltonian: can arbitrary variations in
the tensors that represent ground state of a Hamiltonian be induced by local
perturbations to the Hamiltonian? Starting from a tensor product state which is
the exact ground state of a Hamiltonian with topological order,
we show that, surprisingly, not all variations of the tensors correspond to the
variation of the ground state caused by local perturbations of the Hamiltonian.
Even in the absence of any symmetry requirement of the perturbed Hamiltonian,
one necessary condition for the variations of the tensors to be physical is
that they respect certain symmetry. We support this claim by
calculating explicitly the change in topological entanglement entropy with
different variations in the tensors. This finding will provide important
guidance to numerical variational study of topological phase and phase
transitions. It is also a crucial step in using TPS to study universal
properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure
Nuclear symmetry energy and the r-mode instability of neutron stars
We analyze the role of the symmetry energy slope parameter on the {\it
r}-mode instability of neutron stars. Our study is performed using both
microscopic and phenomenological approaches of the nuclear equation of state.
The microscopic ones include the Brueckner--Hartree--Fock approximation, the
well known variational equation of state of Akmal, Pandharipande and Ravenhall,
and a parametrization of recent Auxiliary Field Diffusion Monte Carlo
calculations. For the phenomenological approaches, we use several Skyrme forces
and relativisic mean field models. Our results show that the {\it r}-mode
instability region is smaller for those models which give larger values of .
The reason is that both bulk () and shear () viscosities increase
with and, therefore, the damping of the mode is more efficient for the
models with larger . We show also that the dependence of both viscosities on
can be described at each density by simple power-laws of the type
and . Using the measured spin
frequency and the estimated core temperature of the pulsar in the low-mass
X-ray binary 4U 1608-52, we conclude that observational data seem to favor
values of larger than MeV if this object is assumed to be outside
the instability region, its radius is in the range () km, and
its mass (). Outside this range it is not possible to
draw any conclusion on from this pulsar.Comment: 10 pages, 6 figures. Version published in Physical Review
Prescription for experimental determination of the dynamics of a quantum black box
We give an explicit prescription for experimentally determining the evolution
operators which completely describe the dynamics of a quantum mechanical black
box -- an arbitrary open quantum system. We show necessary and sufficient
conditions for this to be possible, and illustrate the general theory by
considering specifically one and two quantum bit systems. These procedures may
be useful in the comparative evaluation of experimental quantum measurement,
communication, and computation systems.Comment: 6 pages, Revtex. Submitted to J. Mod. Op
Induced Nested Galactic Bars Inside Assembling Dark Matter Halos
We investigate the formation and evolution of nested bar systems in disk
galaxies in a cosmological setting by following the development of an isolated
dark matter (DM) and baryon density perturbation. The disks form within the
assembling triaxial DM halos and the feedback from the stellar evolution is
accounted for in terms of supernovae and OB stellar winds. Focusing on a
representative model, we show the formation of an oval disk and of a first
generation of nested bars with characteristic sub-kpc and a few kpc sizes. The
system evolves through successive dynamical couplings and decouplings, forcing
the gas inwards and settles in a state of resonant coupling. The inflow rate
can support a broad range of activity within the central kpc, from quasar- to
Seyfert-types, supplemented by a vigorous star formation as a by-product. The
initial bar formation is triggered in response to the tidal torques from the
triaxial DM halo, which acts as a finite perturbation. This first generation of
bars does not survive for more than 4--5 Gyr: by that time the secondary bar
has totally dissolved, while the primary one has very substantially weakened,
reduced to a fat oval. This evolution is largely due to chaos introduced by the
interaction of the multiple non-axisymmetric components.Comment: 4 pages, 4 figures, 1 mpeg animation. To be published by the
Astrophysical Journal Letters. The animation can be found at
http://www.pa.uky.edu/~shlosman/research/galdyn/movies.html Replaced with an
updated version (small text corrections
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