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 p...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.展开更多
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 conser...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.展开更多
<正> A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemicalpotentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to ...<正> A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemicalpotentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe two-flavor normal quark matter.Depending on whether m_0/A,the ratio of dynamical quark mass in vacuum and the 3Dmomentum cutoff in the loop integrals,is less or greater than 0.413,the phase transition will be of the second or firstorder.A complete phase diagram of u quark chemical potential versus m_0 is given.With the electrical neutralityconstraint,the region where the second order phase transition happens will be wider than the one without electricalneutrality limitation.The results also show that,for the value of m_0/A from QCD phenomenology,the phase transitionmust be of the first order.展开更多
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 ...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.展开更多
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 nuc...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.展开更多
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. Struc...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.展开更多
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 co...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.展开更多
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 s...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.展开更多
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 ato...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.展开更多
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 o...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.展开更多
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...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.展开更多
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-bran...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.展开更多
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...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.展开更多
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 simpli...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<sup>±</sup>, Z<sup>0</sup> are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin<sup>2</sup> θ<sub>w</sub> =1/4 can be given.展开更多
We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to c...We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to compute the dependence of the chiral condensate at finite temperature,E and B.We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude.We also consider the effect of equilibration of chiral density,n_5,produced by axial anomaly on the critical temperature.The equilibration of n_5 allows for the introduction of the chiral chemical potential,u_5,which is computed selfconsistently as a function of temperature and field strength.We find that even if the chiral medium is produced by the fields the thermodynamics,with particular reference to the inverse catalysis induced by the external fields,it is not very affected by n_5 at least if the average u_5,at equilibrium is not too large.展开更多
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 09CX04018A)
文摘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.
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475113
文摘<正> A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemicalpotentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe two-flavor normal quark matter.Depending on whether m_0/A,the ratio of dynamical quark mass in vacuum and the 3Dmomentum cutoff in the loop integrals,is less or greater than 0.413,the phase transition will be of the second or firstorder.A complete phase diagram of u quark chemical potential versus m_0 is given.With the electrical neutralityconstraint,the region where the second order phase transition happens will be wider than the one without electricalneutrality limitation.The results also show that,for the value of m_0/A from QCD phenomenology,the phase transitionmust be of the first order.
文摘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.
基金Supported by Hunan Provincial Natural Science Foundation of China(2015JJ2005)the Science Research Foundation of Education Department of Hunan Province(15C0029)+1 种基金the National Natural Science Foundation of China(11103001)the construct program of the key discipline in Hunan province
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China(11775123,11890712,11747312,11475062)the National Key R&D Program of China(2018YFA0306503)
文摘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.
基金Supported by National Natural Science Foundation of China(11775049,11275048)the China Jiangsu Provincial Natural Science Foundation(BK20131286)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12135003)。
文摘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.
文摘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.
基金National Natural Science Foundation of China and the Doctor Education Fund of the Ministry of China
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No 10475034).
文摘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.
文摘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.
文摘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<sup>±</sup>, Z<sup>0</sup> are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin<sup>2</sup> θ<sub>w</sub> =1/4 can be given.
基金supported by the CAS President’s International Fellowship Initiative(No.2015PM008)the National Natural Science Foundation of China(Nos.11135011 and 11575190)
文摘We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to compute the dependence of the chiral condensate at finite temperature,E and B.We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude.We also consider the effect of equilibration of chiral density,n_5,produced by axial anomaly on the critical temperature.The equilibration of n_5 allows for the introduction of the chiral chemical potential,u_5,which is computed selfconsistently as a function of temperature and field strength.We find that even if the chiral medium is produced by the fields the thermodynamics,with particular reference to the inverse catalysis induced by the external fields,it is not very affected by n_5 at least if the average u_5,at equilibrium is not too large.