H.G. Miller

Chemical equilibration in heavy-ion collisions

Abstract We examine the question of chemical equilibration in heavy-ion collisions by comparing hadron production ratios from the NA35 and WA85 Collaborations with those calculated in an equilibrium thermodynamic model of hadron product. This model includes hadron interactions in a mean field approximation, hadron resonance decays and the effects of finite system size. We find that the mean values obtained from the calculation are in good agreement with experiment, which suggests that the system formed in the heavy-ion collision was in chemical equilibrium. We find that the NA35 and WA85 data are compatible with a freeze-out temperature and baryon number density of 170 MeV and 0.1 fm −3 respectively. In addition, we calculate the statistical fluctuations in the hadron production rates obtained from the model.

On the relationship between the Fisher-Frieden-Soffer arrow of time, and the behaviour of the Boltzmann and Kullback entropies

Abstract We provide a new derivation of the H-theorem satisfied by Fishers information measure (I) for the diffusion equation and show that the ensuing monotonically decreasing behaviour of I yields, in turn, an H-theorem involving the second time derivative of the standard Boltzmann-Gibbs-Shannon entropy S. An upper bound for S(t) is obtained from this latter relation. Additionally, it is demonstrated that, under certain conditions, the behaviour of I may be related to that of the relative information measure of Kullback. This latter result is generalized to the case of the Fokker-Planck equation.

A lower bound for Fisher's information measure

Abstract For systems of particles that are in a general state of motion a lower bound to Fishers information measure is derived with the help of a recently established upper bound to the entropy increase. This bound to the information measure is the basis for a variational principle devised to determine unknown probability distributions. A simple example illustrates this idea.

Generalized statistics and high-Tc superconductivity

Introducing the generalized, non-extensive statistics proposed by Tsallis [1], into the standard s-wave pairing BCS theory of superconductivity in 2D yields a reasonable description of many of the main properties of high temperature superconductors, provided some allowance is made for non-phonon mediated interactions. The discovery of superconductivity in the copper oxides in 1986 [2] and the subsequent race for even higher critical temperatures (125K by 1993 [3, 4]) raised hopes for the application of superconducting phenomenon at operating temperatures approaching room temperature. The inability of the Bardeen-Cooper-Schrieffer (BCS) model [5] to describe superconductivity in these materials satisfactorily, appears to indicate that we are dealing with a completely different class of superconductors. Various theoretical models have been proposed to explain this phenomenom, ranging from dwave superconductivity [6, 7] to models incorporating non-phononic coupling mechanisms [8, 9, 10, 11]. Different degrees of success have been achieved in explaining specific aspects of these high-Tc materials, but no inclusive model exists. A number of characteristics must be incorporated in any such model. Certainly the main common denominator in all high-Tc materials is the large anisotropy in the crystal structure, resulting in conduction electron states in the CuO2 planes being very nearly two-dimensional in character. It is therefore reasonable to assume that this is essential for the high critical

A semi-empirical determination of the properties of nuclear matter

Abstract The temperature dependence of the coefficients in the semi-empirical mass formula has been determined from a least squares fit to the canonical ensemble average of the excitation energy for nuclei throughout the periodic table. The low temperature behavior in the leading coefficient, the bulk energy density, is in disagreeement with current parameterizations used in the equations of state for symmetric nuclear matter. Peaked structure in the specific heat occurs at a temperature of approximately 0.5 MeV in agreement with theoretical predictions of the critical temperature of a pairing phase transition in nuclear matter.

Hadronic gas interpretation of NA35 and WA85 results

Abstract Particle ratios, as recently measured by the NA35 and WA85 Collaborations, are interpreted within the framework of chemically equilibrated hadronic gas models. The lower and upper experimental bounds of the NA35s Λ /Λ and Ks0/Λ ratios are compatible with a hadronic gas at temperatures T⩾174 MeV, and freeze-out baryon densities nB⩾0.16 fm−3. The Ξ−/Λ, Ξ − / Λ , Λ /Λ and Ξ − /Ξ − ratios, as reported by WA85, can be fitted using the same hadronic gas model with T⩾178 MeV and nB⩾0.16 fm−3.

Freeze-out in the E802 and NA35 experiments

Abstract We compare the thermodynamic conditions at freeze-out obtained from the results of E802 and NA35 Collaborations using an equilibrium thermodynamic model of hadron production. This model includes hadron interactions in a mean field approximation, hadron resonance decays and the effects of finite system size. The large discrepancies in freeze-out temperatures and densities may be qualitatively understood in terms of a simple kinetic model, and are the result of the very different meson to baryon ratios in the two experiments. This arises from the different incident energies, and thus initial compositions of the hadron gas, in the two experiments.

Correlated finite temperature mean field approximations

Abstract A correlated finite temparature mean field approximation is compared with the exact canonical, the conventional finite temperature Hartree-Fock (grand canonical) and canomical finite temperature Hartree-Fock results in Ne for the first time with a realistic interaction. The thermal behavior obtained in the correlated approach differs substantially from that given by mean field calculations. There are no sharp transitions and the system remains deformed at all temperatures, in agreement with exact canonical results.

Kaon condensation in hadron gas models

Abstract We investigate the possibility of kaon condensation in dense hadronic matter within the context of equilibrium hadron gas models, where different approximations for the hadron hard-core repulsive interaction are made. We find that models which approximate the interactions by an excluded volume formalism always lead to a kaon condensate, while the occurrence of such a condensate in models which include the interactions via a mean field approximation is related to the number of hadron species which interact. Moreover, hadron gas models which are consistent with the presently available experimental data do not allow for kaon condensation in a physically realistic region.

Finite size effects in the deconfinement transition

The concepts of quark confinement and asymptotic freedom inherent in models of strongly interacting matter at the sub-hadronic level have lead to a great deal of interest in the associated deconfinement phase transition, i.e. the transition from a gas of Hadrons to a hot plasma of deconfined quarks and gluons. The possibility of obtaining energy densities which are large enough to cause deconfinement in ultra-relativistic heavy ion collisions has acted as one of the main stimuli to interest in such collisions, from both the experimental and theoretical points of view.