351 research outputs found
Applications of DFT to the theory of twentieth-century harmony
Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip
Fourier phase and pitch-class sum
Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.Accepted manuscrip
Theoretical model for ultracold molecule formation via adaptive feedback control
We investigate pump-dump photoassociation of ultracold molecules with
amplitude- and phase-modulated femtosecond laser pulses. For this purpose a
perturbative model for the light-matter interaction is developed and combined
with a genetic algorithm for adaptive feedback control of the laser pulse
shapes. The model is applied to the formation of 85Rb2 molecules in a
magneto-optical trap. We find for optimized pulse shapes an improvement for the
formation of ground state molecules by more than a factor of 10 compared to
unshaped pulses at the same pump-dump delay time, and by 40% compared to
unshaped pulses at the respective optimal pump-dump delay time. Since our model
yields directly the spectral amplitudes and phases of the optimized pulses, the
results are directly applicable in pulse shaping experiments
Global analysis of data on the spin-orbit coupled and states of Cs2
We present experimentally derived potential curves and spin-orbit interaction
functions for the strongly perturbed and
states of the cesium dimer. The results are based on data from several sources.
Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used
some time ago in the Laboratoire Aim\'{e} Cotton primarily to study the state. More recent work at Tsinghua University provides
information from moderate resolution spectroscopy on the lowest levels of the
states as well as additional high resolution data. From
Innsbruck University, we have precision data obtained with cold Cs
molecules. Recent data from Temple University was obtained using the
optical-optical double resonance polarization spectroscopy technique, and
finally, a group at the University of Latvia has added additional LIF FTS data.
In the Hamiltonian matrix, we have used analytic potentials (the Expanded Morse
Oscillator form) with both finite-difference (FD) coupled-channels and discrete
variable representation (DVR) calculations of the term values. Fitted diagonal
and off-diagonal spin-orbit functions are obtained and compared with {\it ab
initio} results from Temple and Moscow State universities
Characterization of the HeCo mutant mouse: a new model of subcortical band heterotopia associated with seizures and behavioral deficits.
In human, neuronal migration disorders are commonly associated with developmental delay, mental retardation, and epilepsy. We describe here a new mouse mutant that develops a heterotopic cortex (HeCo) lying in the dorsolateral hemispheric region, between the homotopic cortex (HoCo) and subcortical white matter. Cross-breeding demonstrated an autosomal recessive transmission. Birthdating studies and immunochemistry for layer-specific markers revealed that HeCo formation was due to a transit problem in the intermediate zone affecting both radially and tangentially migrating neurons. The scaffold of radial glial fibers, as well as the expression of doublecortin is not altered in the mutant. Neurons within the HeCo are generated at a late embryonic age (E18) and the superficial layers of the HoCo have a correspondingly lower cell density and layer thickness. Parvalbumin immunohistochemistry showed the presence of gamma-aminobutyric acidergic cells in the HeCo and the mutant mice have a lowered threshold for the induction of epileptic seizures. The mutant showed a developmental delay but, in contrast, memory function was relatively spared. Therefore, this unique mouse model resembles subcortical band heterotopia observed in human. This model represents a new and rare tool to better understand cortical development and to investigate future therapeutic strategies for refractory epilepsy
Ab initio calculation of the KRb dipole moments
The relativistic configuration interaction valence bond method has been used
to calculate permanent and transition electric dipole moments of the KRb
heteronuclear molecule as a function of internuclear separation. The permanent
dipole moment of the ground state potential is found to be
0.30(2) at the equilibrium internuclear separation with excess negative
charge on the potassium atom. For the potential the dipole moment
is an order of magnitude smaller (1 Cm) In addition, we
calculate transition dipole moments between the two ground-state and
excited-state potentials that dissociate to the K(4s)+Rb(5p) limits. Using this
data we propose a way to produce singlet KRb molecules by a
two-photon Raman process starting from an ultracold mixture of doubly
spin-polarized ground state K and Rb atoms. This Raman process is only allowed
due to relativistic spin-orbit couplings and the absence of gerade/ungerade
selection rules in heteronuclear dimers.Comment: 16 pages, 7 figure
Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
We generalize the concept of separable dual-space Gaussian pseudopotentials
to the relativistic case. This allows us to construct this type of
pseudopotential for the whole periodic table and we present a complete table of
pseudopotential parameters for all the elements from H to Rn. The relativistic
version of this pseudopotential retains all the advantages of its
nonrelativistic version. It is separable by construction, it is optimal for
integration on a real space grid, it is highly accurate and due to its analytic
form it can be specified by a very small number of parameters. The accuracy of
the pseudopotential is illustrated by an extensive series of molecular
calculations
Optimal trapping wavelengths of Cs molecules in an optical lattice
The present paper aims at finding optimal parameters for trapping of Cs
molecules in optical lattices, with the perspective of creating a quantum
degenerate gas of ground-state molecules. We have calculated dynamic
polarizabilities of Cs molecules subject to an oscillating electric field,
using accurate potential curves and electronic transition dipole moments. We
show that for some particular wavelengths of the optical lattice, called "magic
wavelengths", the polarizability of the ground-state molecules is equal to the
one of a Feshbach molecule. As the creation of the sample of ground-state
molecules relies on an adiabatic population transfer from weakly-bound
molecules created on a Feshbach resonance, such a coincidence ensures that both
the initial and final states are favorably trapped by the lattice light,
allowing optimized transfer in agreement with the experimental observation
Photoassociation spectroscopy of cold calcium atoms
Photoassociation spectroscopy experiments on 40Ca atoms close to the
dissociation limit 4s4s 1S0 - 4s4p 1P1 are presented. The vibronic spectrum was
measured for detunings of the photoassociation laser ranging from 0.6 GHz to 68
GHz with respect to the atomic resonance. In contrast to previous measurements
the rotational splitting of the vibrational lines was fully resolved. Full
quantum mechanical numerical simulations of the photoassociation spectrum were
performed which allowed us to put constraints on the possible range of the
calcium scattering length to between 50 a_0 and 300 a_0
Dark resonances for ground state transfer of molecular quantum gases
One possible way to produce ultracold, high-phase-space-density quantum gases
of molecules in the rovibronic ground state is given by molecule association
from quantum-degenerate atomic gases on a Feshbach resonance and subsequent
coherent optical multi-photon transfer into the rovibronic ground state. In
ultracold samples of Cs_2 molecules, we observe two-photon dark resonances that
connect the intermediate rovibrational level |v=73,J=2> with the rovibrational
ground state |v=0,J=0> of the singlet ground state potential.
For precise dark resonance spectroscopy we exploit the fact that it is possible
to efficiently populate the level |v=73,J=2> by two-photon transfer from the
dissociation threshold with the stimulated Raman adiabatic passage (STIRAP)
technique. We find that at least one of the two-photon resonances is
sufficiently strong to allow future implementation of coherent STIRAP transfer
of a molecular quantum gas to the rovibrational ground state |v=0,J=0>.Comment: 7 pages, 4 figure
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