22 research outputs found
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
We present a general scheme for the study of frustration in quantum systems.
We introduce a universal measure of frustration for arbitrary quantum systems
and we relate it to a class of entanglement monotones via an exact inequality.
If all the (pure) ground states of a given Hamiltonian saturate the inequality,
then the system is said to be inequality saturating. We introduce sufficient
conditions for a quantum spin system to be inequality saturating and confirm
them with extensive numerical tests. These conditions provide a generalization
to the quantum domain of the Toulouse criteria for classical frustration-free
systems. The models satisfying these conditions can be reasonably identified as
geometrically unfrustrated and subject to frustration of purely quantum origin.
Our results therefore establish a unified framework for studying the
intertwining of geometric and quantum contributions to frustration.Comment: 8 pages, 1 figur
On the temporal order of first-passage times in one-dimensional lattice random walks
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing modified Bessel functions of the first kind. By using several transformations simpler integrals are obtained from which for two and three particles asymptotic approximations are derived for large values of the parameters. Expressions of the probability for n particles are also derive
A comparison of propofol and chloral hydrate for sedation of young children during magnetic resonance imaging scans
Flooding countries and destroying dams
In many applications of terrain analysis, pits or local minima are considered artifacts that must be removed before the terrain can be used. Most of the existing methods for local minima removal work only for raster terrains. In this paper we consider algorithms to remove local minima from polyhedral terrains, by modifying the heights of the vertices. To limit the changes introduced to the terrain, we try to minimize the total displacement of the vertices. Two approaches to remove local minima are analyzed: lifting vertices and lowering vertices. For the former we show that all local minima in a terrain with n vertices can be removedintheoptimalwayinO(n log n) time. For the latter we prove that the problem is NP-hard, and present an approximation algorithm with factor 2 ln k, wherek is the number of local minima in the terrain