5,406 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
Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
We propose to measure nonadiabaticity of molecular quantum dynamics
rigorously with the quantum fidelity between the Born-Oppenheimer and fully
nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies
in situations where other criteria, such as the energy gap criterion or the
extent of population transfer, fail. We further propose to estimate this
quantum fidelity efficiently with a generalization of the dephasing
representation to multiple surfaces. Two variants of the multiple-surface
dephasing representation (MSDR) are introduced, in which the nuclei are
propagated either with the fewest-switches surface hopping (FSSH) or with the
locally mean field dynamics (LMFD). The LMFD can be interpreted as the
Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used
previously in the nonadiabatic semiclassical initial value representation. In
addition to propagating an ensemble of classical trajectories, the MSDR
requires evaluating nonadiabatic couplings and solving the Schr\"{o}dinger (or
more generally, the quantum Liouville-von Neumann) equation for a single
discrete degree of freedom. The MSDR can be also used to measure the importance
of other terms present in the molecular Hamiltonian, such as diabatic
couplings, spin-orbit couplings, or couplings to external fields, and to
evaluate the accuracy of quantum dynamics with an approximate nonadiabatic
Hamiltonian. The method is tested on three model problems introduced by Tully,
on a two-surface model of dissociation of NaI, and a three-surface model
including spin-orbit interactions. An example is presented that demonstrates
the importance of often-neglected second-order nonadiabatic couplings.Comment: 14 pages, 4 figures, submitted to J. Chem. Phy
The method of Gaussian weighted trajectories. V. On the 1GB procedure for polyatomic processes
In recent years, many chemical reactions have been studied by means of the
quasi-classical trajectory (QCT) method within the Gaussian binning (GB)
procedure. The latter consists in "quantizing" the final vibrational actions in
Bohr spirit by putting strong emphasis on the trajectories reaching the
products with vibrational actions close to integer values. A major drawback of
this procedure is that if N is the number of product vibrational modes, the
amount of trajectories necessary to converge the calculations is ~ 10^N larger
than with the standard QCT method. Applying it to polyatomic processes is thus
problematic. In a recent paper, however, Czako and Bowman propose to quantize
the total vibrational energy instead of the vibrational actions [G. Czako and
J. M. Bowman, J. Chem. Phys., 131, 244302 (2009)], a procedure called 1GB here.
The calculations are then only ~ 10 times more time-consuming than with the
standard QCT method, allowing thereby for considerable numerical saving. In
this paper, we propose some theoretical arguments supporting the 1GB procedure
and check its validity on model test cases as well as the prototype four-atom
reaction OH+D_2 -> HOD+D
Coherent Control and Entanglement in the Attosecond Electron Recollision Dissociation of D2+
We examine the attosecond electron recollision dissociation of D2+ recently
demonstrated experimentally [H. Niikura et al., Nature (London) 421, 826
(2003)] from a coherent control perspective. In this process, a strong laser
field incident on D2 ionizes an electron, accelerates the electron in the laser
field to eV energies, and then drives the electron to recollide with the parent
ion, causing D2+ dissociation. A number of results are demonstrated. First, a
full dimensional Strong Field Approximation (SFA) model is constructed and
shown to be in agreement with the original experiment. This is then used to
rigorously demonstrate that the experiment is an example of coherent pump-dump
control. Second, extensions to bichromatic coherent control are proposed by
considering dissociative recollision of molecules prepared in a coherent
superposition of vibrational states. Third, by comparing the results to similar
scenarios involving field-free attosecond scattering of independently prepared
D2+ and electron wave packets, recollision dissociation is shown to provide an
example of wave-packet coherent control of reactive scattering. Fourth, this
analysis makes clear that it is the temporal correlations between the continuum
electron and D2+ wave packet, and not entanglement, that are crucial for the
sub-femtosecond probing resolution demonstrated in the experiment. This result
clarifies some misconceptions regarding the importance of entanglement in the
recollision probing of D2+. Finally, signatures of entanglement between the
recollision electron and the atomic fragments, detectable via coincidence
measurements, are identified
Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers
Free energies and other thermodynamical quantities are investigated in
canonical and grand canonical ensembles of statistical mechanics involving
unstable states which are described by the generalized eigenstates with complex
energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is
applied to the systems containing parabolic potential barriers (PPB's). The
entropy and energy productions from PPB systems are studied. An equilibrium for
a chemical process described by reactions is also
discussed.Comment: 14 pages, AmS-LaTeX, no figur
Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy
We study the quantum dynamics of a two-level system driven by a pulse that
starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and
induces an adiabatic evolution for larger amplitudes. This problem is analyzed
in terms of lifting of degeneracy for rising amplitudes. It is solved exactly
for the case of linear and exponential rising. Approximate solutions are given
in the case of power law rising. This allows us to determine approximative
formulas for the lineshape of resonant excitation by various forms of pulses
such as truncated trig-pulses. We also analyze and explain the various
superpositions of states that can be obtained by the Half Stark Chirped Rapid
Adiabatic Passage (Half-SCRAP) process.Comment: 21 pages, 12 figure
Strong-field dipole resonance. I. Limiting analytical cases
We investigate population dynamics in N-level systems driven beyond the
linear regime by a strong external field, which couples to the system through
an operator with nonzero diagonal elements. As concrete example we consider the
case of dipolar molecular systems. We identify limiting cases of the
Hamiltonian leading to wavefunctions that can be written in terms of ordinary
exponentials, and focus on the limits of slowly and rapidly varying fields of
arbitrary strength. For rapidly varying fields we prove for arbitrary that
the population dynamics is independent of the sign of the projection of the
field onto the dipole coupling. In the opposite limit of slowly varying fields
the population of the target level is optimized by a dipole resonance
condition. As a result population transfer is maximized for one sign of the
field and suppressed for the other one, so that a switch based on flopping the
field polarization can be devised. For significant sign dependence the
resonance linewidth with respect to the field strength is small. In the
intermediate regime of moderate field variation, the integral of lowest order
in the coupling can be rewritten as a sum of terms resembling the two limiting
cases, plus correction terms for N>2, so that a less pronounced sign-dependence
still exists.Comment: 34 pages, 1 figur
From angle-action to Cartesian coordinates: A key transformation for molecular dynamics
The transformation from angle-action variables to Cartesian coordinates is a
crucial step of the (semi) classical description of bimolecular collisions and
photo-fragmentations. The basic reason is that dynamical conditions
corresponding to experiments are ideally generated in angle-action variables
whereas the classical equations of motion are ideally solved in Cartesian
coordinates by standard numerical approaches. To our knowledge, the previous
transformation is available in the literature only for triatomic systems. The
goal of the present work is to derive it for polyatomic ones.Comment: 10 pages, 11 figures, submitted to J. Chem. Phy
The quality of different types of child care at 10 and 18 months. A comparison between types and factors related to quality.
The quality of care offered in four different types of non-parental child care to 307 infants at 10 months old and 331 infants at 18 months old was compared and factors associated with higher quality were identified. Observed quality was lowest in nurseries at each age point, except that at 18 months they offered more learning activities. There were few differences in the observed quality of care by child-minders, grandparents and nannies, although grandparents had somewhat lower safety and health scores and offered children fewer activities. Cost was largely unrelated to quality of care except in child-minding, where higher cost was associated with higher quality. Observed ratios of children to adults had a significant impact on quality of nursery care; the more infants or toddlers each adult had to care for, the lower the quality of the care she gave them. Mothers' overall satisfaction with their child's care was positively associated with its quality for home-based care but not for nursery settings
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