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Register a new userQuantum morphogenesis: A variation on Thoms catastrophe theory
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Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to phenomena of morphogenesis which may occur in non-commutative systems. Several explicit exactly solvable models are presented, including `birth and death of an organism and `development of complementary properties.
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A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
Quantum theory is a well-defined local theory with a clear interpretation. No measurement problem or any other foundational matters are waiting to be settled.
This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers on subtree features. The second approach visualizes the global metric structure of datasets through low-distortion embedding into hyperbolic planes in the style of multidimensional scaling. A case study is made on a dataset of airway trees in relation to Chronic Obstructive Pulmonary Disease.
We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Andersons orthogonality catastrophe can be witnessed.
Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. Simple models defined by contact topology, known as elastic network models, have been used to model a variety of systems, but the validation is typically limited to individual modes for a single protein. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational variance. Normal modes from four simple elastic network model potentials and from the CHARMM forcefield are calculated for a data set of 83 diverse, ultrahigh resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, the methods that consider all atoms have a clear edge at prediction of directionality, and the CHARMM potential produces the best agreement. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. This was illustrated by computing the dynamic correlation matrices from different potentials for a PDZ domain structure. Comparison of normal mode results with anisotropic temperature factors opens the possibility of using ultrahigh resolution crystallographic data as a quantitative measure of molecular flexibility. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity. Comparison of the dynamic correlation matrices suggests that a combination of topological and chemical potentials may help identify residues in which chemical forces make large contributions to intramolecular coupling.
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