3,185 research outputs found
Sewing sound quantum flesh onto classical bones
Semiclassical transformation theory implies an integral representation for
stationary-state wave functions in terms of angle-action variables
(). It is a particular solution of Schr\"{o}dinger's time-independent
equation when terms of order and higher are omitted, but the
pre-exponential factor in the integrand of this integral
representation does not possess the correct dependence on . The origin of
the problem is identified: the standard unitarity condition invoked in
semiclassical transformation theory does not fix adequately in a
factor which is a function of the action written in terms of and
. A prescription for an improved choice of this factor, based on
succesfully reproducing the leading behaviour of wave functions in the vicinity
of potential minima, is outlined. Exact evaluation of the modified integral
representation via the Residue Theorem is possible. It yields wave functions
which are not, in general, orthogonal. However, closed-form results obtained
after Gram-Schmidt orthogonalization bear a striking resemblance to the exact
analytical expressions for the stationary-state wave functions of the various
potential models considered (namely, a P\"{o}schl-Teller oscillator and the
Morse oscillator).Comment: RevTeX4, 6 page
The Open Cluster Distance Scale: A New Empirical Approach
We present new BVRI photometry for a sample of 54 local G and K stars with accurate Hipparcos parallaxes in the metallicity range -0.4 < [Fe/H] < +0.3. We use this sample to develop a completely model-independent main sequence (MS) fitting method which we apply to 4 open clusters - the Hyades, Praesepe, the Pleiades and NGC 2516 - which all have direct Hipparcos parallax distance determinations. Comparison of our MS-fitting results with distances derived from Hipparcos parallaxes enables us to explore whether the discrepancy between the Hipparcos distance scale and other MS-fitting methods found for some clusters is a consequence of model assumptions. We find good agreement between our results and the Hipparcos ones for the Hyades and Praesepe. For the Pleiades and NGC 2516, when adopting the solar abundance determined from spectroscopy, we find significant disagreement at a level similar to that found by other MS-fitting studies. However, the colour-colour relationship for both these clusters suggests that their metallicity is significantly subsolar. Since the MS-fitting method relies on matching the cluster colours to a template MS, we argue that, when applying this method, the appropriate metallicity to adopt is the photometric subsolar one, not the solar abundance indicated by spectroscopy. Adopting photometric metallicities for all 4 clusters, we find complete agreement with the Hipparcos results and hence we conclude that the mismatch between the spectroscopic and photometric abundances for the Pleiades and NGC 2516 is responsible for the discrepancies in distance estimates found by previous studies. The origin of this mismatch in abundance scales remains an unsolved problem and some possible causes are discussed
Friedmann Equation for Brans Dicke Cosmology
In the context of Brans-Dicke scalar tensor theory of gravitation, the
cosmological Friedmann equation which relates the expansion rate of the
universe to the various fractions of energy density is analyzed rigorously. It
is shown that Brans-Dicke scalar tensor theory of gravitation brings a
negligible correction to the matter density component of Friedmann equation.
Besides, in addition to and in standard
Einstein cosmology, another density parameter, , is
expected by the theory. This implies that if is found to
be nonzero, data will favor this model instead of the standard Einstein
cosmological model with cosmological constant and will enable more accurate
predictions for the rate of change of Newtonian gravitational constant in the
future.Comment: minor reference change
A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling
Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK âOctopusâ, EPSRC âReactor Core-Structure Re-location Modelling for Severe Nuclear Accidentsâ) and Horizon 2020 âIn-Vessel Melt Retentionâ. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC âMulti-Scale Exploration of Multi-phase Physics in Flowsâ. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD
Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity
© 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
A multiscale view on inverse statistics and gain/loss asymmetry in financial time series
Researchers have studied the first passage time of financial time series and
observed that the smallest time interval needed for a stock index to move a
given distance is typically shorter for negative than for positive price
movements. The same is not observed for the index constituents, the individual
stocks. We use the discrete wavelet transform to illustrate that this is a long
rather than short time scale phenomenon -- if enough low frequency content of
the price process is removed, the asymmetry disappears. We also propose a new
model, which explain the asymmetry by prolonged, correlated down movements of
individual stocks
Signatures of chaotic and non-chaotic-like behaviour in a non-linear quantum oscillator through photon detection
The driven non-linear duffing osillator is a very good, and standard, example
of a quantum mechanical system from which classical-like orbits can be
recovered from unravellings of the master equation. In order to generated such
trajectories in the phase space of this oscillator in this paper we use a the
quantum jumps unravelling together with a suitable application of the
correspondence principle. We analyse the measured readout by considering the
power spectra of photon counts produced by the quantum jumps. Here we show that
localisation of the wave packet from the measurement of the oscillator by the
photon detector produces a concomitant structure in the power spectra of the
measured output. Furthermore, we demonstrate that this spectral analysis can be
used to distinguish between different modes of the underlying dynamics of the
oscillator.Comment: 7 pages, 6 figure
Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation
The scientific objectives of the Lisa Technology Package (LTP) experiment, on
board of the LISA Pathfinder mission, demand for an accurate calibration and
validation of the data analysis tools in advance of the mission launch. The
levels of confidence required on the mission outcomes can be reached only with
an intense activity on synthetically generated data. A flexible procedure
allowing the generation of cross-correlated stationary noise time series was
set-up. Multi-channel time series with the desired cross correlation behavior
can be generated once a model for a multichannel cross-spectral matrix is
provided. The core of the procedure is the synthesis of a noise coloring
multichannel filter through a frequency-by-frequency eigendecomposition of the
model cross-spectral matrix and a Z-domain fit. The common problem of initial
transients in noise time series is solved with a proper initialization of the
filter recursive equations. The noise generator performances were tested in a
two dimensional case study of the LTP dynamics along the two principal channels
of the sensing interferometer.Comment: Accepted for publication in Physical Review D (http://prd.aps.org/
Optical discrimination between spatial decoherence and thermalization of a massive object
We propose an optical ring interferometer to observe environment-induced
spatial decoherence of massive objects. The object is held in a harmonic trap
and scatters light between degenerate modes of a ring cavity. The output signal
of the interferometer permits to monitor the spatial width of the object's wave
function. It shows oscillations that arise from coherences between energy
eigenstates and that reveal the difference between pure spatial decoherence and
that coinciding with energy transfer and heating. Our method is designed to
work with a wide variety of masses, ranging from the atomic scale to
nano-fabricated structures. We give a thorough discussion of its experimental
feasibility.Comment: 2 figure
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