1,888 research outputs found
Integrals of monomials over the orthogonal group
A recursion formula is derived which allows to evaluate invariant integrals
over the orthogonal group O(N), where the integrand is an arbitrary finite
monomial in the matrix elements of the group. The value of such an integral is
expressible as a finite sum of partial fractions in . The recursion formula
largely extends presently available integration formulas for the orthogonal
group.Comment: 9 pages, no figure
Universal model for exoergic bimolecular reactions and inelastic processes
From a rigorous multichannel quantum-defect formulation of bimolecular
processes, we derive a fully quantal and analytic model for the total rate of
exoergic bimolecular reactions and/or inelastic processes that is applicable
over a wide range of temperatures including the ultracold regime. The theory
establishes a connection between the ultracold chemistry and the regular
chemistry by showing that the same theory that gives the quantum threshold
behavior agrees with the classical Gorin model at higher temperatures. In
between, it predicts that the rates for identical bosonic molecules and
distinguishable molecules would first decrease with temperature outside of the
Wigner threshold region, before rising after a minimum is reached.Comment: 5 pages, 1 figur
Examining a Ripple Effect: Do Spouses’ Behavior Changes Predict Each Other’s Weight Loss?
Background. Including spouses in obesity treatment has been found to promote weight loss. We assessed whether spouses’ diet and activity changes impacted each other’s weight loss when both members attended an active weight loss program (TOGETHER) or only the primary participant attended treatment (ALONE).
Methods. Heterosexual couples () enrolled in an 18-month randomized controlled weight loss trial were weighed and completed measures of dietary intake and physical activity at baseline and 6 months. We conducted dyadic data analyses using the Actor-Partner Interdependence Model.
Results. Participants’ weight loss was not predicted by their partners’ behavior changes. However, partners’ weight loss was predicted by their participants’ changes in calorie and fat intake. When partners were coupled with a participant who did not reduce their own calorie and fat intake as much, these partners had higher weight loss when treated in the TOGETHER group but lower weight loss when they were untreated in the ALONE group. There were no reciprocal effects found with physical activity changes.
Conclusions. Direct treatment had the greatest impact on participants and partners who were treated. Untreated partners’ weight losses were positively impacted by their spouses’ dietary changes, suggesting a ripple effect from treated spouses to their untreated partners
Monomial integrals on the classical groups
This paper presents a powerfull method to integrate general monomials on the
classical groups with respect to their invariant (Haar) measure. The method has
first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)],
and is here used to obtain similar integration formulas for the unitary and the
unitary symplectic group. The integration formulas turn out to be of similar
form. They are all recursive, where the recursion parameter is the number of
column (row) vectors from which the elements in the monomial are taken. This is
an important difference to other integration methods. The integration formulas
are easily implemented in a computer algebra environment, which allows to
obtain analytical expressions very efficiently. Those expressions contain the
matrix dimension as a free parameter.Comment: 16 page
Low rank perturbations and the spectral statistics of pseudointegrable billiards
We present an efficient method to solve Schr\"odinger's equation for
perturbations of low rank. In particular, the method allows to calculate the
level counting function with very little numerical effort. To illustrate the
power of the method, we calculate the number variance for two pseudointegrable
quantum billiards: the barrier billiard and the right triangle billiard
(smallest angle ). In this way, we obtain precise estimates for the
level compressibility in the semiclassical (high energy) limit. In both cases,
our results confirm recent theoretical predictions, based on periodic orbit
summation.Comment: 4 page
Fidelity amplitude of the scattering matrix in microwave cavities
The concept of fidelity decay is discussed from the point of view of the
scattering matrix, and the scattering fidelity is introduced as the parametric
cross-correlation of a given S-matrix element, taken in the time domain,
normalized by the corresponding autocorrelation function. We show that for
chaotic systems, this quantity represents the usual fidelity amplitude, if
appropriate ensemble and/or energy averages are taken. We present a microwave
experiment where the scattering fidelity is measured for an ensemble of chaotic
systems. The results are in excellent agreement with random matrix theory for
the standard fidelity amplitude. The only parameter, namely the perturbation
strength could be determined independently from level dynamics of the system,
thus providing a parameter free agreement between theory and experiment
A random matrix approach to decoherence
In order to analyze the effect of chaos or order on the rate of decoherence
in a subsystem, we aim to distinguish effects of the two types of dynamics by
choosing initial states as random product states from two factor spaces
representing two subsystems. We introduce a random matrix model that permits to
vary the coupling strength between the subsystems. The case of strong coupling
is analyzed in detail, and we find no significant differences except for very
low-dimensional spaces.Comment: 11 pages, 5 eps-figure
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