Construction of one-gluon and one-pion exchange forces in the chiral bag

In the framework of a spherical chiral bag model we use the one-gluon exchange mechanism (inside) and the one-pion exchange (on the surface) to derive an interaction between quarks. In order to apply the force together with two-component (Pauli-spinor) wave functions, which considerably facilitates the elimination of center-of-mass motion, two approximately unitary transformations are performed. The salient features of the derived force are that the relativistic nature is maintained and that quark and gluon confinement is made explicit by force terms originating from the bag boundary conditions.     

Surface collective motion in the soliton bag model

Surface monopole vibration of the baryon is investigated on the basis of the soliton bag model. We derive a relativistic lagrangian for the motion, of which the mass parameter is proportional to the square of the bag radius. With the use of the semi-classical quantization, the energy spectra of the P₁₁ and P₃₃ resonances are reproduced fairly well by our model.     

Valence quark distributions in the soliton bag model

Valence quark distributions are calculated in a momentum projected version of the soliton bag model. These distributions are evolved to Q²=15 GeV² using QCD perturbation theory, where they are compared with experiment. Substantial agreement is achieved.     

Meson exchange currents in the Skyrme soliton model

The isovector meson exchange currents are investigated on the basis of the product ansatz in the Skyrme model. It is shown that the standard one-pion-exchange currents are correctly reproduced as a limiting approximation to more general expressions derived here. We discuss interesting consequences of the spatially extended structure of the nucleon, which is naturally incorporated in the present treatment. It is also pointed out that there exists a simple analytical relation between the isoscalar exchange current of the Skyrme model and the standard ρπγ exchange current.     

Self-consistent treatment of the Anderson model

TheN-fold degenerate Anderson single impurity model in the infiniteU limit is treated by means of the irreducible Green functions method. In this approach a derivation of an exact Dyson equation and an exact self-energy operator is possible. The necessity of introducing auxiliary fields, such as slave-bosons is avoided.     

Self-consistent treatment of the polaron damping in the Holstein model

Using the Holstein model, the damping of the localized polaron state and the small polaron conductivity are represented by the series of contributions from the multiphonon processes in which the polaron damping is taken into account. The self-consistent treatment of the damping shows the enhancement of the small-polaron relaxation rate by the quantum fluctuations of the lattice corresponding to the energy non-conserving phonon processes. The conditions for the polaron localization as well as the dependence of the d.c. conductivity on the electron transfer integral are discussed.     

Gluon exchange corections to the nucleon magnetic moment in the mit bag model

We have calculated gluon exchange corrections to the nucleon magnetic moment predictions of the MIT bag model. The sizeable coupling constant $\text{g}{}^2{}_{\mathrm{c}}\text{/}\text{4π=0.5}$ does not produce an enormous correction (≈10%), but it is in the wrong direction to ameliorate the present 30% disagreement with experiment.     

The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

Energy exchange in fast optical soliton collisions as a random cascade model

We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the τq exponents from multifractal theory and by the Cramér function S(x). We find that the nth moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of τq or S(x).     

密度依赖口袋常数下奇异物质的热力学自洽处理及其对混合星性质的影响

在MTT口袋模型的基础上采用密度依赖口袋常数,给出了奇异夸克物质的热力学关系,并用于描述奇异夸克物质及混合星内的夸克相,研究了奇异星、混合星的性质.结果表明,密度依赖口袋常数下,奇异夸克物质的压强公式中有一个附加项,而能量密度中则没有,从而保证了系统的热力学自洽性.在新的热力学关系下,奇异夸克物质的状态方程变软,相应的奇异星的引力质量和对应的半径均变小;混合星的状态方程也变软,其质量变小,而对应的半径也变小.说明经热力学自洽处理后该模型对中子星的状态方程及相应的质量-半径关系等都有显著的影响.     

Vacuum energy in the bag model

The vacuum energy of the Yang-Mills field is examined for the conditions of the bag model. The dominance of high-frequency effects results in a vacuum energy that decomposes naturally into a volume energy, a surface energy, and higher shape energies. These quantities are identified with the parameters of the bag model. The imposition of confining boundary conditions for all frequencies is shown to be inconsistent since this would result in the bag constant and certain of the shape tensions being infinite. The manner in which the boundary conditions should be relaxed at high frequency is discussed. The most naive procedure for relaxing the boundary conditions, which is to apply confining conditions only on modes of frequency less than some cutoff frequency, results in a negative bag constant and surface tension and would render the vacuum unstable against the spontaneous breaking of Poincaré invariance. Consideration of the manner by which the interacting electromagnetic field avoids a similar instability suggests that a more realistic way to relax the boundary conditions on the bag surface is to endow the vacuum exterior to the bag with a frequency-dependent dielectric constant and magnetic permeability. In this picture the stability of the vacuum is restored, the surface tension is finite and positive, and the bag constant is zero at least to lowest order in the coupling. It is pointed out that the fermion contributions to the bag constant and the surface tension may relate to the spontaneous breaking of chiral invariance. The aim throughout is to examine the bag model, as it relates to vacuum energy, strictly in its own terms with an emphasis on questions of principle.All too often is heard the alibi that since the theory itself is only approximate, the mathematics need be no better. In truth the opposite follows. Granted that the model represents but a part of nature, we are to find what such an ideal picture implies, a result strictly derived serves to test the model; a false result proves nothing but the failure of the theorist. To call an error by a sweeter name does not correct it. The oversimplification or extension afforded by the model is not error: the model, if well made, shows at least how the universe might behave, but logical errors bring us no closer to the reality of any universe. (Truesdell and Toupin 1960).     

Vacuum condensates in the bag model

The consequences of having quark and gluon condensates inside a MIT bag are investigated. We show that one naturally expects a state dependent bag constant and a colour-magnetic interaction term ～R². This gives the possibility of having a small strong coupling constant α_s inside the bag.     

Neutron-rich hypernuclei in the chiral soliton model

The binding energies of neutron-rich strangeness S = ?1 hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron-rich nuclei takes place at not large values of atomic (baryon) numbers, A = B ?? ??10. This effect becomes stronger with increasing isospin of nuclides, and for the ??nuclear variant?? of the model with rescaled Skyrme constant e. Binding energies of _?? ⁸ He and recently discovered _?? ⁶ H satisfactorily agree with data. Hypernuclei _?? ⁷ H, _?? ⁹ He are predicted to be bound stronger in comparison with their nonstrange analogues ⁷H, ⁹He; hypernuclei _?? ¹⁰ Li, _?? ¹¹ LI, _?? ¹² Be, _?? ¹³ Be, etc. are bound stronger in the nuclear variant of the model.     

Self-consistently thermodynamic treatment for strange quark matter in the effective mass bag model

In the framework of the effective mass bag model (EMBM) we have performed the thermodynamical treatment for strange quark matter (SQM) self-consistently, which overcomes the inconsistencies in the thermodynamical properties of the system. Because of the existence of the pressure extra term, the SQM equation of state (EOS) becomes stiffer comparing with the one for the original EMBM. It is interesting to find that in our treatment the SQM EOS is almost independent of the strong coupling constant g . In this case the SQM EOS seems to get back to the EOS for the original MIT bag model. However, this treatment still has influence on the EOS for hybrid star matter and the corresponding mass-radius relations. With the increase of the strong coupling constant g , the EOS for hybrid star matter gets obviously stiff. From our treatment we notice that the pressure extra term can make a hybrid star more compact than the one described in the original EMBM and this model is more suitable to describe the hybrid stars with small radii.     

Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.