9,503 research outputs found
On the Executability of Interactive Computation
The model of interactive Turing machines (ITMs) has been proposed to
characterise which stream translations are interactively computable; the model
of reactive Turing machines (RTMs) has been proposed to characterise which
behaviours are reactively executable. In this article we provide a comparison
of the two models. We show, on the one hand, that the behaviour exhibited by
ITMs is reactively executable, and, on the other hand, that the stream
translations naturally associated with RTMs are interactively computable. We
conclude from these results that the theory of reactive executability subsumes
the theory of interactive computability. Inspired by the existing model of ITMs
with advice, which provides a model of evolving computation, we also consider
RTMs with advice and we establish that a facility of advice considerably
upgrades the behavioural expressiveness of RTMs: every countable transition
system can be simulated by some RTM with advice up to a fine notion of
behavioural equivalence.Comment: 15 pages, 0 figure
Conserving Approximations in Time-Dependent Density Functional Theory
In the present work we propose a theory for obtaining successively better
approximations to the linear response functions of time-dependent density or
current-density functional theory. The new technique is based on the
variational approach to many-body perturbation theory (MBPT) as developed
during the sixties and later expanded by us in the mid nineties. Due to this
feature the resulting response functions obey a large number of conservation
laws such as particle and momentum conservation and sum rules. The quality of
the obtained results is governed by the physical processes built in through
MBPT but also by the choice of variational expressions. We here present several
conserving response functions of different sophistication to be used in the
calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio
Total energies from variational functionals of the Green function and the renormalized four-point vertex
We derive variational expressions for the grand potential or action in terms
of the many-body Green function which describes the propagation of
particles and the renormalized four-point vertex which describes the
scattering of two particles in many-body systems. The main ingredient of the
variational functionals is a term we denote as the -functional which plays
a role analogously to the usual -functional studied by Baym (G.Baym,
Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in
many-body systems. We show that any -derivable theory is also
-derivable and therefore respects the conservation laws. We further set
up a computational scheme to obtain accurate total energies from our
variational functionals without having to solve computationally expensive sets
of self-consistent equations. The input of the functional is an approximate
Green function and an approximate four-point vertex
obtained at a relatively low computational cost. The
variational property of the functional guarantees that the error in the total
energy is only of second order in deviations of the input Green function and
vertex from the self-consistent ones that make the functional stationary. The
functionals that we will consider for practical applications correspond to
infinite order summations of ladder and exchange diagrams and are therefore
particularly suited for applications to highly correlated systems. Their
practical evaluation is discussed in detail.Comment: 21 pages, 10 figures. Physical Review B (accepted
Initialization by measurement of a two-qubit superconducting circuit
We demonstrate initialization by joint measurement of two transmon qubits in
3D circuit quantum electrodynamics. Homodyne detection of cavity transmission
is enhanced by Josephson parametric amplification to discriminate the two-qubit
ground state from single-qubit excitations non-destructively and with 98.1%
fidelity. Measurement and postselection of a steady-state mixture with 4.7%
residual excitation per qubit achieve 98.8% fidelity to the ground state, thus
outperforming passive initialization.Comment: 5 pages, 4 figures, and Supplementary Information (7 figures, 1
table
Long-range interactions and the sign of natural amplitudes in two-electron systems
In singlet two-electron systems the natural occupation numbers of the
one-particle reduced density matrix are given as squares of the natural
amplitudes which are defined as the expansion coefficients of the two-electron
wave function in a natural orbital basis. In this work we relate the sign of
the natural amplitudes to the nature of the two-body interaction. We show that
long-range Coulomb-type interactions are responsible for the appearance of
positive amplitudes and give both analytical and numerical examples that
illustrate how the long-distance structure of the wave function affects these
amplitudes. We further demonstrate that the amplitudes show an avoided crossing
behavior as function of a parameter in the Hamiltonian and use this feature to
show that these amplitudes never become zero, except for special interactions
in which infinitely many of them can become zero simultaneously when changing
the interaction strength. This mechanism of avoided crossings provides an
alternative argument for the non-vanishing of the natural occupation numbers in
Coulomb systems.Comment: 10 pages, 4 figure
A deconvolution map-making method for experiments with circular scanning strategies
Aims. To investigate the performance of a deconvolution map-making algorithm
for an experiment with a circular scanning strategy, specifically in this case
for the analysis of Planck data, and to quantify the effects of making maps
using simplified approximations to the true beams. Methods. We present an
implementation of a map-making algorithm which allows the combined treatment of
temperature and polarisation data, and removal of instrumental effects, such as
detector time constants and finite sampling intervals, as well as the
deconvolution of arbitrarily complex beams from the maps. This method may be
applied to any experiment with a circular scanning-strategy. Results.
Low-resolution experiments were used to demonstrate the ability of this method
to remove the effects of arbitrary beams from the maps and to demonstrate the
effects on the maps of ignoring beam asymmetries. Additionally, results are
presented of an analysis of a realistic full-scale simulated data-set for the
Planck LFI 30 GHz channel. Conclusions. Our method successfully removes the
effects of the beams from the maps, and although it is computationally
expensive, the analysis of the Planck LFI data should be feasible with this
approach.Comment: 14 pages, 14 figures, accepte
Numerical simulations on the motion of atoms travelling through a standing-wave light field
The motion of metastable helium atoms travelling through a standing light
wave is investigated with a semi-classical numerical model. The results of a
calculation including the velocity dependence of the dipole force are compared
with those of the commonly used approach, which assumes a conservative dipole
force. The comparison is made for two atom guiding regimes that can be used for
the production of nanostructure arrays; a low power regime, where the atoms are
focused in a standing wave by the dipole force, and a higher power regime, in
which the atoms channel along the potential minima of the light field. In the
low power regime the differences between the two models are negligible and both
models show that, for lithography purposes, pattern widths of 150 nm can be
achieved. In the high power channelling regime the conservative force model,
predicting 100 nm features, is shown to break down. The model that incorporates
velocity dependence, resulting in a structure size of 40 nm, remains valid, as
demonstrated by a comparison with quantum Monte-Carlo wavefunction
calculations.Comment: 9 pages, 4 figure
Optimising the multiplex factor of the frequency domain multiplexed readout of the TES-based microcalorimeter imaging array for the X-IFU instrument on the Athena Xray observatory
Athena is a space-based X-ray observatory intended for exploration of the hot
and energetic universe. One of the science instruments on Athena will be the
X-ray Integrated Field Unit (X-IFU), which is a cryogenic X-ray spectrometer,
based on a large cryogenic imaging array of Transition Edge Sensors (TES) based
microcalorimeters operating at a temperature of 100mK. The imaging array
consists of 3800 pixels providing 2.5 eV spectral resolution, and covers a
field of view with a diameter of of 5 arc minutes. Multiplexed readout of the
cryogenic microcalorimeter array is essential to comply with the cooling power
and complexity constraints on a space craft. Frequency domain multiplexing has
been under development for the readout of TES-based detectors for this purpose,
not only for the X-IFU detector arrays but also for TES-based bolometer arrays
for the Safari instrument of the Japanese SPICA observatory. This paper
discusses the design considerations which are applicable to optimise the
multiplex factor within the boundary conditions as set by the space craft. More
specifically, the interplay between the science requirements such as pixel
dynamic range, pixel speed, and cross talk, and the space craft requirements
such as the power dissipation budget, available bandwidth, and electromagnetic
compatibility will be discussed
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