arXiv subjects
Publications and source records attributed to J. M. Eisenberg.
A derivation is given of the Boltzmann-Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of transport equations in terms of rigorous field-theory descriptions, or, as in this case, exact nonrelativistic formulations.
We review recent achievements in the solution of the initial-value problem for quantum back-reaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining back-reaction has to do with applications to theoretical models of production of the quark-gluon plasma, though we here address practicable solutions for back-reaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features, like plasma oscillations and plateaus in the current, appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.
We investigate the hadronic cooling of a quark droplet within a microscopic model. The color flux tube approach is used to describe the hadronization of the quark phase. The model reproduces experimental particle ratios equally well compared to a static thermal hadronic source. Furthermore, the dynamics of the decomposition of a quark-gluon plasma is investigated and time dependent particle ratios are found.
We study here hot nuclear matter in the quark meson coupling (QMC) model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar and vector mesons. The equation of state of nuclear matter including the composite nature of the nucleons is calculated at finite temperatures. The calculations are done taking into account the medium-dependent bag constant. Nucleon properties at finite temperatures as calculated here are found to be appreciably different from the value at $T=0.$
Preequilibrium parton production following an ultrarelativistic nucleus--nucleus collision is studied in terms of the decay of a strong chromoelectric field which generates pairs through the Schwinger mechanism. Back-reaction of the partons with the field is included and a model transport equation containing a collision term is solved for the central rapidity region based on an approximation in which the partons relax to a thermal distribution.
We study hot nuclear matter in a model based on nucleon interactions deriving from the exchange of scalar and vector mesons. The main new feature of our work is the treatment of the scale breaking of quantum chromodynamics through the introduction of a dilaton field. Although the dilaton effects are quite small quantitatively, they affect the high-temperature phase transition appreciably. We find that inclusion of the dilaton leads to a metastable high-density state at zero pressure, similar to that found by Glendenning who considered instead the admixture of higher baryon resonances.
Within the skyrmion approach for the nucleon-nucleon force, difficulties have been experienced in obtaining an isoscalar attractive spin-orbit potential, in parallel to the problems of finding attraction in the isoscalar central potential. We here study the spin-orbit force using a skyrmion with four- and six-derivative stabilizing terms in the lagrangian as well as with the crucial addition of a dilaton. With these features present the spin-orbit force proves to be attractive as does the central potential. In the absence of the dilaton, attraction can also be found for the spin-orbit potential but only at the expense of a greatly over-emphasized term with six derivatives and a continuing absence of attraction in the central potential.
Earlier work reported on the existence of a term within a generalized skyrmion approach that yields appreciable spin content for the proton. Unfortunately there is no accessible experiment that can fix the coefficient of this term directly; plausible but highly uncertain values for it gave a result for the spin content loosely consistent with the currently measured $ΔΣ= 0.27\pm 0.13.$ We here attempt to narrow the range of values for this coefficient by performing global fits to all the parameters of the generalized Skyrme lagrangian while requiring reasonable results for the baryon octet and decuplet masses and octet magnetic moments. This requirement fixes the coefficient loosely, and we find that parameter sets that fit the baryon masses and magnetic moments yield proton spin content near $ΔΣ\sim 0.15.$
A system is studied in which initially a strong classical electric field exists within an infinitely-long cylinder and no charges are present. Subsequently, within the cylinder, pairs of charged particles tunnel out from the vacuum and the current produced through their acceleration by the field acts back on the field, setting up plasma oscillations. This yields a rough model of phenomena that may occur in the pre-equilibrium formation phase of a quark-gluon plasma. In an infinite volume, this back-reaction has been studied in a field-theory description, and it has been found that the results of a full calculation of this sort are well represented in a much simpler transport formalism. It is the purpose here to explore that comparison for a situation involving a cylindrical volume of given radius.
It is well known that in lowest order the skyrmion model of the nucleon gives vanishing spin content. With new data indicating a proton spin content $ΔΣ= 0.22\pm 0.14,$ it is an increasing challenge to find ways in which the skyrmion can move away from the null result. We show here that a particular term in the skyrmion lagrangian in SU(3) involving six derivatives of the field can, with plausible parameters, yield a spin content consistent with present experiment.
We consider a two-nucleon system described by two different skyrmion models that provide attraction for the central NN potential. One of these models is based on the product ansatz and the other on dilaton coupling. Within these models we ask the question, To what degree does the nucleon swell or shrink when the internucleon separation distance is appropriate to attraction or repulsion? We find typically swelling of 3 to 4 percent for central attraction of some 40 to 50 MeV.
Based on the equal-time Wigner function for the Klein-Gordon field, we discuss analytically the mechanism of pair creation in a classical electromagnetic field including back-reaction. It is shown that the equations of motion for the Wigner function can be reduced to a variable-frequency oscillator. The pair-creation rate results then from a calculation analogous to barrier penetration in nonrelativistic quantum mechanics. The Wigner function allows one to utilize this treatment for the formulation of an effective transport theory for the back-reaction problem with a pair-creation source term including Bose enhancement.
We study pair production from a strong electric field in boost-invariant coordinates as a simple model for the central rapidity region of a heavy-ion collision. We derive and solve the renormalized equations for the time evolution of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $τ= \sqrt{t^2-z^2}$. We find that a relativistic transport theory with a Schwinger source term modified to take Pauli blocking (or Bose enhancement) into account gives a good description of the numerical solution to the field equations. We also compute the renormalized energy-momentum tensor of the produced particles and compare the effective pressure, energy and entropy density to that expected from hydrodynamic models of energy and momentum flow of the plasma.