74 research outputs found
On the consequences of the fact that atomic levels have a certain width
This note presents two ideas. The first one is that quantum theory has a
fundamentally perturbative basis but leads to nonperturbative states which it
would seem natural to take into account in the foundation of a theory of
quantum phenomena. The second one consists in questioning the validity of the
present notion of time. Both matters are related to the fact that atomic levels
have a certain width. This note is presented qualitatively so as to evidence
its main points, independently of the models on which these have been tested.Comment: 8 page
Exact Solution Methods for the -item Quadratic Knapsack Problem
The purpose of this paper is to solve the 0-1 -item quadratic knapsack
problem , a problem of maximizing a quadratic function subject to two
linear constraints. We propose an exact method based on semidefinite
optimization. The semidefinite relaxation used in our approach includes simple
rank one constraints, which can be handled efficiently by interior point
methods. Furthermore, we strengthen the relaxation by polyhedral constraints
and obtain approximate solutions to this semidefinite problem by applying a
bundle method. We review other exact solution methods and compare all these
approaches by experimenting with instances of various sizes and densities.Comment: 12 page
Engineering Branch-and-Cut Algorithms for the Equicut Problem
A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application
Weak and strong coupling regimes, vacuum Rabi splitting and two types of resonances
For two discrete-level quantum systems in interaction, we follow the displacement in the complex plane of the eigen-energies of the compound system when the excited level of one of the two systems is enlarged. These new points are usually called resonances and describe mixed unstable states. This allows us to define and to calculate a critical value of the coupling constant which separates two well-known coupling regimes. These two regimes are thus described in a unified way.
In the study, resonances which are usually not taken into account occur. They are studied in the large continuum case provided by the coupling of the hydrogen atom to the states of the transverse electromagnetic field in the vacuum. We justify that some of these resonances be neglected in this case
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