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Taiichi Yamada - One of the best experts on this subject based on the ideXlab platform.
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A new Formalism of nuclear matter: tensor-optimized Fermi sphere method
'Springer Science and Business Media LLC', 2021Co-Authors: Taiichi YamadaAbstract:A new Formalism of nuclear matter, called “tensor-optimized Fermi sphere (TOFS) method”, is developed to handle the nuclear matter using a bare interaction among nucleons. In this Formalism, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function F, $$\varPsi _{N}=[\sum _{n=0}^{N} (1/n!)F^{n}]\varPhi _{0}$$, where F can induce central, spin-isospin, tensor, spin-orbit, etc. correlation, and $$\varPhi _{0}$$ is the uncorrelated Fermi-gas wave function. The validity of our Formalism is based on a linked-cluster expansion theorem established in the TOFS theory with Hermitian Form. The connection between $$\varPsi _{N}$$ and an exponential type correlated nuclear matter wave function, $$\varPsi _{ex}=\exp (F) \varPhi _{0}$$, is emphasized to lead to the theorem. The framework of TOFS is a variational method, in which the correlation function F is determined by minimizing the energy per particle in nuclear matter with respect to the nuclear matter wave function $$\varPsi _{N}$$. The first application of the TOFS theory is perFormed to study the property of nuclear matter using the Argonne V4’ NN potential. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $$\rho \simeq 0.20$$$$\hbox {fm}^{-3}$$, in comparison with other methods such as the Brueckner-Hartree-Fock (BHF) approach. We discuss the explicit contributions of many-body terms in the total energy, and indicate the importance of higher-body terms
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tensor optimized fermi sphere method for nuclear matter power series correlated wave function and a cluster expansion
Annals of Physics, 2019Co-Authors: Taiichi YamadaAbstract:Abstract A new Formalism, called “tensor optimized Fermi sphere (TOFS) method”, is developed to treat the nuclear matter using a bare interaction among nucleons. In this method, the correlated nuclear matter wave function is taken to be a power series type, Ψ N = [ ∑ n = 0 N ( 1 ∕ n ! ) F n ] Φ 0 and an exponential type, Ψ ex = exp ( F ) Φ 0 , with the uncorrelated Fermi-gas wave function Φ 0 , where the correlation operator F can induce central, spin–isospin, tensor, etc. correlations, and Ψ ex corresponds to a limiting case of Ψ N ( N → ∞ ). In the TOFS Formalism based on Hermitian Form, it is shown that the energy per particle in nuclear matter with Ψ ex can be expressed in terms of a linked-cluster expansion. On the basis of these results, we present the Formula of the energy per particle in nuclear matter with Ψ N . We call the N th-order TOFS calculation for evaluating the energy with Ψ N , where the correlation functions are optimally determined in the variation of the energy. The TOFS theory is applied for the study of symmetric nuclear matter using a central NN potential with short-range repulsion. The calculated results are fairly consistent to those of other theories such as the Brueckner–Hartree–Fock approach etc.
Jiawei Zhang - One of the best experts on this subject based on the ideXlab platform.
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on approximating complex quadratic optimization problems via semidefinite programming relaxations
Integer Programming and Combinatorial Optimization, 2005Co-Authors: Jiawei ZhangAbstract:In this paper we study semidefinite programming (SDP) models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian Form. These problems capture a class of well–known combinatorial optimization problems, as well as problems in control theory. For instance, they include Max–3–Cut where the Laplacian matrix is positive semidefinite (in particular, some of the edge weights can be negative). We present a generic algorithm and a unified analysis of the SDP relaxations which allow us to obtain good approximation guarantees for our models. Specifically, we give an $(k sin(\frac{\pi}{k}))^{2}/(4\pi)$ –approximation algorithm for the discrete problem where the decision variables are k–ary and the objective matrix is positive semidefinite. To the best of our knowledge, this is the first known approximation result for this family of problems. For the continuous problem where the objective matrix is positive semidefinite, we obtain the well–known π/4 result due to [2], and independently, [12]. However, our techniques simplify their analyses and provide a unified framework for treating these problems. In addition, we show for the first time that the integrality gap of the SDP relaxation is precisely π/4. We also show that the unified analysis can be used to obtain an O(1/log n)–approximation algorithm for the continuous problem in which the objective matrix is not positive semidefinite.
Igor Zelenko - One of the best experts on this subject based on the ideXlab platform.
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a canonical Form for pairs consisting of a Hermitian Form and a self adjoint antilinear operator
Linear Algebra and its Applications, 2020Co-Authors: David Sykes, Igor ZelenkoAbstract:Abstract Motivated by a problem in local differential geometry of Cauchy–Riemann (CR) structures of hypersurface type, we find a canonical Form for pairs consisting of a nondegenerate Hermitian Form and a self-adjoint antilinear operator, or, equivalently, consisting of a nondegenerate Hermitian Form and a symmetric bilinear Form. This generalizes the only previously known results on simultaneous normalization of such pairs, namely, the results of [2] on simultaneous diagonalization of these pairs in the case where the Hermitian Form is positive definite and of [11] , where a criterion for simultaneous diagonalization is given.
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a canonical Form for pairs consisting of a Hermitian Form and a self adjoint antilinear operator
arXiv: Complex Variables, 2019Co-Authors: David Sykes, Igor ZelenkoAbstract:Motivated by a problem in local differential geometry of Cauchy--Riemann (CR) structures of hypersurface type, we find a canonical Form for pairs consisting of a nondegenerate Hermitian Form and a self-adjoint antilinear operator, or, equivalently, consisting of a nondegenerate Hermitian Form and a symmetric bilinear Form. This generalizes the only previously known results on simultaneous normalization of such pairs, namely, the results of Benedetti and Cragnolini (1984) on simultaneous diagonalization of these pairs in the case where the Hermitian Form is positive definite and of Hong and Horn (1986), where a criterion for simultaneous diagonalization is given.
Evgenii L Bashkirov - One of the best experts on this subject based on the ideXlab platform.
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linear groups of degree 4 over a quaternion division ring that contain the special unitary group of a skew Hermitian Form with maximal witt index
Communications in Algebra, 2014Co-Authors: Evgenii L BashkirovAbstract:The paper describes subgroups of the general linear group GL 4(D) over a quaternion division ring D that contain the special unitary group of degree 4 over a non-central subfield of D. The connections between these subgroups and the spinor groups of appropriate symmetric bilinear Forms are established.
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irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup diag t3 k φ0 1
Journal of Algebra, 2005Co-Authors: Evgenii L BashkirovAbstract:Abstract Let F be a field of characteristic ≠2, D a quaternion division algebra over F, K a subfield of D, σ an involutory automorphism of K, Φ 0 a non-degenerate σ-skew-Hermitian Form in three variables over K whose Witt index is 1. Suppose that K contains a subfield K 0 of F such that each element of K 0 is invariable under σ and F is algebraic over K 0 . We study the irreducible subgroups of GL 4 ( D ) that contain the subgroup diag ( T 3 ( K , Φ 0 ) , 1 ) .
Nick Salter - One of the best experts on this subject based on the ideXlab platform.
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linear central filtrations and the image of the burau representation
Geometriae Dedicata, 2021Co-Authors: Nick SalterAbstract:The Burau representation is a fundamental bridge between the braid group and diverse other topics in mathematics. A 1974 question of Birman asks for a description of the image; in this paper we give an approximate answer. Since a 1984 paper of Squier it has been known that the Burau representation preserves a certain Hermitian Form. We show that the Burau image is dense in this unitary group relative to a topology induced by a naturally-occurring filtration. We expect that the methods of the paper should extend to many other representations of the braid group.
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linear central filtrations and the image of the burau representation
arXiv: Geometric Topology, 2019Co-Authors: Nick SalterAbstract:The Burau representation is a fundamental bridge between the braid group and diverse other topics in mathematics. A 1974 question of Birman asks for a description of the image; in this paper we give a "strong approximation" to the answer. Since a 1984 paper of Squier it has been known that the Burau representation preserves a certain Hermitian Form. We show that the Burau image is dense in this unitary group relative to a topology induced by a naturally-occurring filtration. We expect that the methods of the paper should extend to many other representations of the braid group and perhaps ultimately inForm the study of knot and link polynomials.