The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Jonas Larson - One of the best experts on this subject based on the ideXlab platform.
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Integrability versus quantum thermalization
Journal of Physics B: Atomic Molecular and Optical Physics, 2013Co-Authors: Jonas LarsonAbstract:Non-Integrability is often taken as a prerequisite for quantum thermalization. Still, a generally accepted definition of quantum Integrability is lacking. With the basis in the driven Rabi model we discuss this careless usage of the term "Integrability" in connection to quantum thermalization. The model would be classified as non-integrable according to the most commonly used definitions, for example, the only preserved quantity is the total energy. Despite this fact, a thorough analysis conjectures that the system will not thermalize. Thus, our findings suggest first of all (i) that care should be paid when linking non-Integrability with thermalization, and secondly (ii) that the standardly used definitions for quantum Integrability are unsatisfactory.
Maria Przybylska - One of the best experts on this subject based on the ideXlab platform.
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Integrability Analysis of the Stretch–Twist–Fold Flow
Journal of Nonlinear Science, 2020Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:We study the Integrability of an eight-parameter family of three-dimensional spherically confined steady Stokes flows introduced by Bajer and Moffatt. This volume-preserving flow was constructed to model the stretch–twist–fold mechanism of the fast dynamo magnetohydrodynamical model. In particular we obtain a complete classification of cases when the system admits an additional Darboux polynomial of degree one. All but one such case are integrable, and first integrals are presented in the paper. The case when the system admits an additional Darboux polynomial of degree one but is not evidently integrable is investigated by methods of differential Galois theory. It is proved that the four-parameter family contained in this case is not integrable in the Jacobi sense, i.e. it does not admit a meromorphic first integral. Moreover, we investigate the Integrability of other four-parameter $${\textit{STF}}$$ STF systems using the same methods. We distinguish all the cases when the system satisfies necessary conditions for Integrability obtained from an analysis of the differential Galois group of variational equations.
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Differential Galois theory and Integrability
arXiv09121046, 2009Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:This paper is an overview of our works which are related to investigations of the Integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of Integrability obstructions for these systems are presented. The first, local ones, are related to the analysis of the differential Galois group of variational equations along a non-equilibrium particular solution. The second, global ones, are obtained from the simultaneous analysis of variational equations related to all particular solutions belonging to a certain class. The marriage of these two types of the Integrability obstructions enables to realise the classification programme of all integrable homogeneous systems. The main steps of the Integrability analysis for systems with two and more degrees of freedom as well as new integrable systems are shown.
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darboux points and Integrability of hamiltonian systems with homogeneous polynomial potential
Journal of Mathematical Physics, 2005Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:In this paper we study the Integrability of natural Hamiltonian systems with a homogeneous polynomial potential. The strongest necessary conditions for their Integrability in the Liouville sense have been obtained by a study of the differential Galois group of variational equations along straight line solutions. These particular solutions can be viewed as points of a projective space of dimension smaller by one than the number of degrees of freedom. We call them Darboux points. We analyze in detail the case of two degrees of freedom. We show that, except for a radial potential, the number of Darboux points is finite and it is not greater than the degree of the potential. Moreover, we analyze cases when the number of Darboux points is smaller than maximal. For two degrees of freedom the above-mentioned necessary condition for Integrability can be expressed in terms of one nontrivial eigenvalue of the Hessian of potential calculated at a Darboux point. We prove that for a given potential these nontrivial ei...
T.s. Huang - One of the best experts on this subject based on the ideXlab platform.
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Enforcing Integrability for surface reconstruction algorithms using belief propagation in graphical models
Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, 2001Co-Authors: N. Petrovic, I. Cohen, B.j. Frey, R. Koetter, T.s. HuangAbstract:Accurate calculation of the three dimensional shape of an object is one of the classic research areas of computer vision. Many of the existing methods are based on surface normal estimation, and subsequent integration of surface gradients. In general, these methods do not produce valid surfaces due to violation of surface Integrability. We introduce a new method for shape reconstruction by integration of valid surface gradient maps. The essence of the new approach is in the strict enforcement of the surface Integrability via belief propagation across graphical models. The graphical model is selected in such a way as to extract information from underlying, possibly noisy, surface gradient estimators, utilize the surface Integrability constraint, and produce the maximum a-posteriori estimate of a valid surface. We demonstrate the algorithm for two classic shape reconstruction techniques; shape-from-shading and photometric stereo. On a set of real and synthetic examples, the new approach is shown to be fast and accurate, in the sense that shape can be rendered even in the presence of high levels of noise and sharp occlusion boundaries.
Andrzej J Maciejewski - One of the best experts on this subject based on the ideXlab platform.
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Integrability Analysis of the Stretch–Twist–Fold Flow
Journal of Nonlinear Science, 2020Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:We study the Integrability of an eight-parameter family of three-dimensional spherically confined steady Stokes flows introduced by Bajer and Moffatt. This volume-preserving flow was constructed to model the stretch–twist–fold mechanism of the fast dynamo magnetohydrodynamical model. In particular we obtain a complete classification of cases when the system admits an additional Darboux polynomial of degree one. All but one such case are integrable, and first integrals are presented in the paper. The case when the system admits an additional Darboux polynomial of degree one but is not evidently integrable is investigated by methods of differential Galois theory. It is proved that the four-parameter family contained in this case is not integrable in the Jacobi sense, i.e. it does not admit a meromorphic first integral. Moreover, we investigate the Integrability of other four-parameter $${\textit{STF}}$$ STF systems using the same methods. We distinguish all the cases when the system satisfies necessary conditions for Integrability obtained from an analysis of the differential Galois group of variational equations.
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Differential Galois theory and Integrability
arXiv09121046, 2009Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:This paper is an overview of our works which are related to investigations of the Integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of Integrability obstructions for these systems are presented. The first, local ones, are related to the analysis of the differential Galois group of variational equations along a non-equilibrium particular solution. The second, global ones, are obtained from the simultaneous analysis of variational equations related to all particular solutions belonging to a certain class. The marriage of these two types of the Integrability obstructions enables to realise the classification programme of all integrable homogeneous systems. The main steps of the Integrability analysis for systems with two and more degrees of freedom as well as new integrable systems are shown.
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darboux points and Integrability of hamiltonian systems with homogeneous polynomial potential
Journal of Mathematical Physics, 2005Co-Authors: Andrzej J Maciejewski, Maria PrzybylskaAbstract:In this paper we study the Integrability of natural Hamiltonian systems with a homogeneous polynomial potential. The strongest necessary conditions for their Integrability in the Liouville sense have been obtained by a study of the differential Galois group of variational equations along straight line solutions. These particular solutions can be viewed as points of a projective space of dimension smaller by one than the number of degrees of freedom. We call them Darboux points. We analyze in detail the case of two degrees of freedom. We show that, except for a radial potential, the number of Darboux points is finite and it is not greater than the degree of the potential. Moreover, we analyze cases when the number of Darboux points is smaller than maximal. For two degrees of freedom the above-mentioned necessary condition for Integrability can be expressed in terms of one nontrivial eigenvalue of the Hessian of potential calculated at a Darboux point. We prove that for a given potential these nontrivial ei...
T. H. Seligman - One of the best experts on this subject based on the ideXlab platform.
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Integrability of the S-matrix versus Integrability of the Hamiltonian
Physics Report, 1997Co-Authors: C. Jung, T. H. SeligmanAbstract:This report reviews the relations between the Integrability properties of the S-matrix and of the Hamiltonian. Particular emphasis is put on the situation where the Hamiltonian has a conserved quantity which is not compatible with the asymptotics and where correspondingly the Integrability does not transfer to the S-matrix. As questions of Integrability are more readily handled in classical dynamics, all developments are first performed classically. Several examples are discussed to illustrate the main points. The quantum mechanical discussion reveals that the eigenphase statistics of the S-matrix depends principally on the chaoticity of the scattering map while basis dependent quantities such as the distribution of matrix elements tend to have random matrix behaviour only in the presence of topological chaos. The relevance of these considerations to the evaluation of scattering data is discussed.
