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Orders of magnitude loss reduction in photonic bandgap fibers by engineering the core surround
We demonstrate how to reduce the loss in photonic bandgap fibers by orders of magnitude by varying the radius of the corner strands in the core surround. As a fundamental working principle we find that changing the corner strand radius can lead to backscattering of light into the fiber core. Selecting an optimal corner strand radius can thus reduce the loss of the fundamental core mode in a specific wavelength range by almost two orders of magnitude when compared to an unmodified cladding structure. Using the optimal corner radius for each transmission window, we observe the low-loss behavior for the first and second bandgaps, with the losses in the second bandgap being even lower than that of the first one. Our approach of reducing the confinement loss is conceptually applicable to all kinds of photonic bandgap fibers including hollow core and all-glass fibers as well as on-chip light cages. Therefore, our concept paves the way to low-loss light guidance in such systems with substantially reduced fabrication complexity
Linear stability analysis of resonant periodic motions in the restricted three-body problem
The equations of the restricted three-body problem describe the motion of a
massless particle under the influence of two primaries of masses and
, , that circle each other with period equal to
. When , the problem admits orbits for the massless particle that
are ellipses of eccentricity with the primary of mass 1 located at one of
the focii. If the period is a rational multiple of , denoted ,
some of these orbits perturb to periodic motions for . For typical
values of and , two resonant periodic motions are obtained for . We show that the characteristic multipliers of both these motions are given
by expressions of the form in the limit . The coefficient is analytic in at and
C(e,p,q)=O(e^{\abs{p-q}}). The coefficients in front of e^{\abs{p-q}},
obtained when is expanded in powers of for the two resonant
periodic motions, sum to zero. Typically, if one of the two resonant periodic
motions is of elliptic type the other is of hyperbolic type. We give similar
results for retrograde periodic motions and discuss periodic motions that
nearly collide with the primary of mass
Model order reduction approaches for infinite horizon optimal control problems via the HJB equation
We investigate feedback control for infinite horizon optimal control problems
for partial differential equations. The method is based on the coupling between
Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is
well-known that HJB equations suffer the so called curse of dimensionality and,
therefore, a reduction of the dimension of the system is mandatory. In this
report we focus on the infinite horizon optimal control problem with quadratic
cost functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati
equation based approach. Finally, we present numerical examples and discuss
several features of the different methods analyzing advantages and
disadvantages of the reduction methods
A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements
A generic model of measurement device which is able to directly measure
commonly used quantum-state characteristics such as fidelity, overlap, purity
and Hilbert-Schmidt distance for two general uncorrelated mixed states is
proposed. In addition, for two correlated mixed states, the measurement
realizes an entanglement witness for Werner's separability criterion. To
determine these observables, the estimation only one parameter - the visibility
of interference, is needed. The implementations in cavity QED, trapped ion and
electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure
Neutron matter at zero temperature with auxiliary field diffusion Monte Carlo
The recently developed auxiliary field diffusion Monte Carlo method is
applied to compute the equation of state and the compressibility of neutron
matter. By combining diffusion Monte Carlo for the spatial degrees of freedom
and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum
Monte Carlo can be used to simulate the ground state of many nucleon systems
(A\alt 100). We use a path constraint to control the fermion sign problem. We
have made simulations for realistic interactions, which include tensor and
spin--orbit two--body potentials as well as three-nucleon forces. The Argonne
and two nucleon potentials plus the Urbana or Illinois
three-nucleon potentials have been used in our calculations. We compare with
fermion hypernetted chain results. We report results of a Periodic Box--FHNC
calculation, which is also used to estimate the finite size corrections to our
quantum Monte Carlo simulations. Our AFDMC results for models of pure
neutron matter are in reasonably good agreement with equivalent Correlated
Basis Function (CBF) calculations, providing energies per particle which are
slightly lower than the CBF ones. However, the inclusion of the spin--orbit
force leads to quite different results particularly at relatively high
densities. The resulting equation of state from AFDMC calculations is harder
than the one from previous Fermi hypernetted chain studies commonly used to
determine the neutron star structure.Comment: 15 pages, 15 tables and 5 figure
Parametrization of projector-based witnesses for bipartite systems
Entanglement witnesses are nonpositive Hermitian operators which can detect
the presence of entanglement. In this paper, we provide a general
parametrization for orthonormal basis of and use it to
construct projector-based witness operators for entanglement detection in the
vicinity of pure bipartite states. Our method to parameterize entanglement
witnesses is operationally simple and could be used for doing symbolic and
numerical calculations. As an example we use the method for detecting
entanglement between an atom and the single mode of quantized field, described
by the Jaynes-Cummings model. We also compare the detection of witnesses with
the negativity of the state, and show that in the vicinity of pure stats such
constructed witnesses able to detect entanglement of the state.Comment: 12 pages, four figure
Spectral properties of the dimerized and frustrated chain
Spectral densities are calculated for the dimerized and frustrated S=1/2
chain using the method of continuous unitary transformations (CUTs). The
transformation to an effective triplon model is realized in a perturbative
fashion up to high orders about the limit of isolated dimers. An efficient
description in terms of triplons (elementary triplets) is possible: a detailed
analysis of the spectral densities is provided for strong and intermediate
dimerization including the influence of frustration. Precise predictions are
made for inelastic neutron scattering experiments probing the S=1 sector and
for optical experiments (Raman scattering, infrared absorption) probing the S=0
sector. Bound states and resonances influence the important continua strongly.
The comparison with the field theoretic results reveals that the sine-Gordon
model describes the low-energy features for strong to intermediate dimerization
only at critical frustration.Comment: 21 page
Electromagnetic transitions of the helium atom in superstrong magnetic fields
We investigate the electromagnetic transition probabilities for the helium
atom embedded in a superstrong magnetic field taking into account the finite
nuclear mass. We address the regime \gamma=100-10000 a.u. studying several
excited states for each symmetry, i.e. for the magnetic quantum numbers
0,-1,-2,-3, positive and negative z parity and singlet and triplet symmetry.
The oscillator strengths as a function of the magnetic field, and in particular
the influence of the finite nuclear mass on the oscillator strengths are shown
and analyzed.Comment: 10 pages, 8 figure
Spin-1/2 J1-J2 model on the body-centered cubic lattice
Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study
the influence of frustration and quantum fluctuations on the magnetic ordering
in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2
model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on
the square lattice, we find for the bcc lattice that frustration and quantum
fluctuations do not lead to a quantum disordered phase for strong frustration.
The results of both approaches (ED, LSWT) suggest a first order transition at
J2/J1 0.7 from the two-sublattice Neel phase at low J2 to a collinear
phase at large J2.Comment: 6.1 pages 7 figure
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