The Experts below are selected from a list of 237 Experts worldwide ranked by ideXlab platform
Francesco Calogero - One of the best experts on this subject based on the ideXlab platform.
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new solvable variants of the goldfish Many Body Problem
Studies in Applied Mathematics, 2016Co-Authors: Francesco CalogeroAbstract:A technique to manufacture solvable variants of the “goldfish” Many-Body Problem is introduced, and several Many-Body Problems yielded by it are identified and discussed, including cases featuring multiperiodic or isochronous dynamics.
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a new solvable Many Body Problem of goldfish type
Journal of Nonlinear Mathematical Physics, 2016Co-Authors: Oksana Bihun, Francesco CalogeroAbstract:A new solvable Many-Body Problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.
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Many Body Problem with quadratic and or inversely quadratic potentials in one and more dimensional spaces some retrospective remarks
Journal of Statistical Physics, 2014Co-Authors: Francesco Calogero, F LeyvrazAbstract:In the context of an ambient space with an arbitrary number \(d\) of dimensions, the Many-Body Problem consisting of an arbitrary number \(N\) of particles confined by a common, external harmonic potential (realizing a container with soft walls) and interacting among themselves and with the environment with arbitrary conservative repulsive forces scaling as the inverse cube of distances, displays a peculiar behaviour: its effective volume oscillates isochronously without damping. We recently discovered this remarkable phenomenon (valid in the context of both classical and quantum mechanics) and discussed its implications in the context of statistical mechanics and thermodynamics; but after publishing these findings we were informed that essentially analogous results had been previously obtained by Lyndell-Bell and Lyndell-Bell. In the present paper, motivated by the need we felt to acknowledge this fact, we also offer some retrospective remarks on the \(N\)-Body Problem with quadratic and/or inversely-quadratic potentials in one- and more-dimensional space.
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an integrable Many Body Problem
Journal of Mathematical Physics, 2011Co-Authors: Francesco CalogeroAbstract:Some years ago, Mikhailov and Sokolov identified as integrable the neat system of two evolution equations U=V2, V=U2, where U ≡ U(t) and V ≡ V(t) are two N × N matrices, N is an arbitrary positive integer, t (“time”) is the independent variable, and superimposed dots indicate the time derivatives. This entails, rather trivially, that the generic solution of the modified version of this model reading U=V2+iωU, V=U2+iωV, with ω an arbitrary positive constant, is completely periodic with period T = 2π/ω (or possibly a period which is an integer multiple of T): “isochrony.” Another, less trivial, consequence of their finding is the observation that the solution of the Many-Body Problem characterized by the Hamiltonian system of N Newtonian evolution equations, xn=−a2xn5+g22∑m=1,m≠nN[(xn−xm)−3+xn+xm−3],n=1,...,N, where xn ≡ xn(t) are N scalar dependent variables and a, g are two arbitrary constants, is simply related to the evolution of the (appropriately rescaled) eigenvalues of a matrix simply related t...
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a complex deformation of the classical gravitational Many Body Problem that features Many completely periodic motions
Journal of Physics A, 2002Co-Authors: Francesco CalogeroAbstract:A complex deformation of the Newtonian equations of motion of the classical gravitational Many-Body Problem is introduced, namely a Many-Body Problem that features a parameter ? and that reduces, when this parameter vanishes, to the standard equations of motion of Newtonian gravitation for an arbitrary number of pointlike bodies with arbitrary masses; and it is shown that when this parameter is instead positive, ?>0, there is an open set of (complex) initial data such that all the (complex) motions originating from it are completely periodic with period T = 2?/?, and that the (infinite) measure of this set is a finite (nonvanishing) fraction of the measure of the entire set of initial data.
Fei Yuan - One of the best experts on this subject based on the ideXlab platform.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
Lecture Notes in Physics, 2017Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schrodinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green’s Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
arXiv: Nuclear Theory, 2016Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schr\"odinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Green's Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
K W Schmid - One of the best experts on this subject based on the ideXlab platform.
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on the use of general symmetry projected hartree fock bogoliubov configurations in variational approaches to the nuclear Many Body Problem
Progress in Particle and Nuclear Physics, 2004Co-Authors: K W SchmidAbstract:Abstract Various variational approaches to the nuclear Many-Body Problem are reviewed, which all use general symmetry-projected Hartree–Fock–Bogoliubov determinants as test configurations. The different approaches vary, however, in the degree of sophistication with which the underlying mean-fields as well as the configuration mixing are determined. The methods are explained in detail and their limitations are discussed. Special attention is payed to the particular symmetry restrictions made in the earlier applications and their consequences. Illustrative examples for some selected applications will be given, and the results, where possible, will be compared to those of alternative approaches. A calculational procedure, which allows one to use phenomenological density-dependent interactions, is reported and its merits and shortcomings are discussed. Finally, the Problem of restoring Galilei invariance in the variational and similar approaches is adressed in some detail.
S K Bogner - One of the best experts on this subject based on the ideXlab platform.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
Lecture Notes in Physics, 2017Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schrodinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green’s Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
arXiv: Nuclear Theory, 2016Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schr\"odinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Green's Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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computational nuclear quantum Many Body Problem the unedf project
Computer Physics Communications, 2013Co-Authors: S K Bogner, Aurel Bulgac, J Carlson, J Engel, George I Fann, R J Furnstahl, Stefano Gandolfi, G Hagen, M Horoi, Calvin W JohnsonAbstract:The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum Many-Body Problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
T D Morris - One of the best experts on this subject based on the ideXlab platform.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
Lecture Notes in Physics, 2017Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schrodinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green’s Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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in medium similarity renormalization group approach to the nuclear Many Body Problem
arXiv: Nuclear Theory, 2016Co-Authors: H Hergert, S K Bogner, Justin G Lietz, T D Morris, S J Novario, Nathan Parzuchowski, Fei YuanAbstract:We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear Many-Body Problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the Many-Body Schr\"odinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Green's Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.