基于Nambu泛函的彩色图像正则化重建

为设计合适的正则化泛函并将其拓展到三维彩色图像空间以及更高维度的信号空间,提出一种基于Nambu泛函的彩色图像正则化重建方法,推导出正则化泛函的Euler-Lagrange方程和数值计算格式。将该方法应用于高维空间的信号重建,克服了各通道单独处理时带来的图像边缘色彩抖动问题。实验结果表明,该方法能够取得良好的图像重建效果。

保积n-元Hom-Nambu-李超代数的性质

给出保积n-元Hom-Nambu-李超代数基本物体的定义,研究了它的性质.构造一类保积n-元Hom-Nambu-李超代数.

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are presented. The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry under infinitesimal transformations is derived. Then, the condition of existence and a kind of Hojman conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.

Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.

Lie symmetry and Hojman conserved quantity of Nambu system

This paper studies the Lie symmetry and Hojman conserved quantity of the Nambu system. The determining equations of Lie symmetry for the system are given. The conditions for existence and the form of the Hojman conserved quantity led by the Lie symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order.

Cosmology of the Nambu-Jona-Lasinio Model

We review the Nambu and Jona-Lasinio model (NJL), proposed long time ago, in the sixties, as a fermion interaction theory with chiral symmetry. The theory is not renormalizable and presents a symmetry breaking due to quantum effects which depends on the strength of the coupling constant. We may associate a phase transition with this symmetry breaking, leading from fermion states to a fermion condensate which can be described effectively by a scalar field. Our purpose in this paper is to exploit the interesting properties of NJL in a different context other than particle physics by studying its cosmological dynamics. We are interested in finding whether possibly the NJL model could be used to describe the still unknown dark energy and/or dark matter, from up to 95% of the energy content of the universe at present time.

Nambu力学系统的Lie对称性及其守恒量

讨论了Nambu力学系统的Lie对称性;建立了系统Lie对称性的确定方程;得到了该对称性引起的守恒量;研究了Lie对称性逆问题.并以Euler方程为例说明了本文的主要结果.

n-Hom-Nambu-李代数的广义导子（英文）

本文给出n-Hom-Nambu-李代数L的广义导子代数GDer(L),拟导子代数QDer(L)和拟型心QC(L),并研究它们的一些基本性质.特别地,我们得到结论GDer(L)=QDer(L)+QC(L).同时,我们得到QDer(L)可以嵌入并成为一个更大的n-Hom-Nambu-李代数的导子.关于n-Hom-Nambu-李代数的型心C(L)的一些结果在本文中也得到了推广.

Nuclear matter and neutron star properties with the extendedNambu-Jona-Lasinio model

An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.

CALCULATION OF NAMBU MECHANICS

In this paper, a fundamental fact that Nambu mechanics is source free was proved. Based on this property, and via the idea of prolongation, finite dimensional Nambu system was prolonged to difference jet bundle. Structure preserving numerical methods of Nambu equations were established. Numerical experiments were presented at last to demonstrate advantages of the structure preserving schemes.

Response functions of hot and dense matter in the Nambu-Jona-Lasino model

We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach.The response functions can be obtained by expanding the generational functional in powers of the external sources.We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics,namely mean-field theory and a beyond-mean-field theory,taking into account mesonic contributions.Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation.We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation,showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons,respectively.Noting that the mesonic contributions are not taken into account in the random phase approximation,we also derive the response functions parallel to the beyond-mean-field theory.We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions:the Aslamazov-Lakin contribution,the self-energy or density-of-state contribution,and the Maki-Thompson contribution.Unlike the equilibrium case,in evaluating the fluctuation contributions,we need to carefully treat the linear terms in external sources and the induced perturbations.In the chiral symmetry breaking phase,we find an additional chiral order parameter induced contribution,which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities.These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover,where the mesonic degrees of freedom are still important.

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M.

Ground-state phase diagram,symmetries,excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions

How many dimensions are there in the universe? Currently, there is confusion about the number of dimensions in the universe. Empirical relations about the number of dimensions in theoretical physics with the concept of common space- time 4 dimensions and unshared dimensions are described in this report.

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.

Evolution of Nielsen-Olesen's String from Chern-Simons Field Theory

We study the topology of Nielsen-Olesen's local field theory of single dual string.Based on the Chern-Simons field theory in three dimensons,we find many strings that can form world sheets in four dimensions.These stringshave important relation to the zero point of the complex scalar field.These world sheets of strings can be expressed bythe topological invariant number,Hopf index,and Brower degree.Nambu-Goto's action is obtained from the Nielsen'saction definitely by using φ-mapping theory.

Topological aspect of Chern-Simons p-branes

By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ（x）, and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.

Numerical Study of the Higgs Mode in the Heisenberg Antiferromagnet on the Square Lattice

The Higgs mode is expected to exist in any system with the spontaneous symmetry breaking of the continuous symmetry. We make numerical study about the Higgs mode in the Heisenberg antiferromagnet on the square lattice by the exact diagonalisation approach. Since the Higgs mode can couple with a pair of the Nambu-Goldstone modes, we calculate the dynamical correlation of the two spin operators, employing the finite temperature Lanczos method. Because the lattice size is severely limited, we make a careful discussion on procedures of finding evidences for the Higgs mode by numerical works. By the discussed procedures, we present numerical results for the dynamical correlation at zero temperature. Then we obtain clear evidences for the Higgs mode of the spin-1/2 Heisenberg antiferromagnet on the square lattice.

An SU(3) Electroweak Unified Model Using Generalized Yang-Mills Theory

Generalized Yang-Mills theory has a covariant derivative which contains both vector and scalar gauge bosons. Based on this theory, we construct an SU(3) unified model of electromagnetic and weak interactions to simplify the Weinberg-Salam model. By using the Nambu-Jona-Lasinio mechanism, the symmetry breaking can be realized dynamically. The masses of W±, Z0 are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin2 θw =1/4 can be given.